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Check updated code, it should work. Don't forget to clear cache

namespace Siarhey\Test\Block\Adminhtml\Promo\Quote\Edit\Tab;

class Actions extends \Magento\Backend\Block\Widget\Form\Generic implements
    \Magento\Backend\Block\Widget\Tab\TabInterface
{
/**
     * @param \Magento\Backend\Block\Template\Context $context
     * @param \Magento\Framework\Registry $registry
     * @param \Magento\Framework\Data\FormFactory $formFactory
     * @param array $data
     */
    public function __construct(
        \Magento\Backend\Block\Template\Context $context,
        \Magento\Framework\Registry $registry,
        \Magento\Framework\Data\FormFactory $formFactory,
        array $data = []
    ) {
        parent::__construct($context, $registry, $formFactory, $data);
    }

    public function getTabLabel()
    {
        return __('Actions');
    }

    public function getTabTitle()
    {
        return __('Actions');
    }

    public function canShowTab()
    {
        return true;
    }

    public function isHidden()
    {
        return false;
    }

    protected function _prepareForm()
    {
        $model = $this->_coreRegistry->registry('current_promo_quote_rule');

        /** @var \Magento\Framework\Data\Form $form */
        $form = $this->_formFactory->create();
        $form->setHtmlIdPrefix('rule_');

        $fieldset = $form->addFieldset(
            'action_fieldset',
            ['legend' => __('Rules')]
        );

        $parentField = $fieldset->addField(
            'simple_action',
            'select',
            [
                'label' => __('Apply'),
                'name' => 'simple_action',
                'options' => [
                    1 => __('Amount 1'),
                    2 => __('Discount 1'),
                    3 => __('Amount 2'),
                    4 => __('Discount 2'),
                ]
            ]
        );

        $childFieldOne = $fieldset->addField(
            'amount',
            'text',
            [
                'name' => 'amount',
                'required' => true,
                'class' => 'validate-not-negative-number',
                'label' => __('Amount')
            ]
        );
        //$model->setAmount($model->getAmount() * 1);

        $childFieldTwo = $fieldset->addField(
            'percent',
            'text',
            ['name' => 'percent', 'label' => __('Percent')]
        );
        //$model->setPercent($model->getPercent() * 1);
 
        $this->setChild(
            'form_after',
            $this->getLayout()->createBlock(
                'Magento\Backend\Block\Widget\Form\Element\Dependence'
            )->addFieldMap(
                $parentField->getHtmlId(),
                $parentField->getName()
            )->addFieldMap(
                $childFieldOne->getHtmlId(),
                $childFieldOne->getName()
            )->addFieldMap(
                $childFieldTwo->getHtmlId(),
                $childFieldTwo->getName()
            )->addFieldDependence(
                $childFieldOne->getName(),
                $parentField->getName(),
                '1,3'
            )->addFieldDependence(
                $childFieldTwo->getName(),
                $parentField->getName(),
                '2,4'
            )
        );

        //$form->setValues($model->getData());

        /*if ($model->isReadonly()) {
            foreach ($fieldset->getElements() as $element) {
                $element->setReadonly(true, true);
            }
        }*/

        $this->setForm($form);
        return parent::_prepareForm();
    }
}

Create a di.xml under adminhtml and add following code:

Basically need to overwrite Magento\Backend\Block\Widget\Form\Element\Dependence class

<preference for="Magento\Backend\Block\Widget\Form\Element\Dependence"
                type="Vendor\Module\Block\Widget\Form\Element\Dependence" />
 

namespace Vendor\Module\Block\Widget\Form\Element;

class Dependence extends \Magento\Backend\Block\Widget\Form\Element\Dependence
{
    /**
     * Register field name dependence one from each other by specified values
     *
     * @param string $fieldName
     * @param string $fieldNameFrom
     * @param \Magento\Config\Model\Config\Structure\Element\Dependency\Field|string $refField
     * @return \Magento\Backend\Block\Widget\Form\Element\Dependence
     */
    public function addFieldDependence($fieldName, $fieldNameFrom, $refField)
    {
        if (!is_object($refField)) {
            /** @var $refField \Magento\Config\Model\Config\Structure\Element\Dependency\Field */
            $refField = $this->_fieldFactory->create(
                ['fieldData' => ['value' => (string)$refField, 'separator' => ','], 'fieldPrefix' => '']
            );
        }
        $this->_depends[$fieldName][$fieldNameFrom] = $refField;
        return $this;
    }
}

Now you can use following way.

->addFieldDependence(
    $childFieldTwo->getName(),
    $parentField->getName(),
    '2,4'
)

Clear Magento2 cache.

Check updated code, it should work.

Check updated code, it should work. Don't forget to clear cache

If your options are (1,2,3,4,5) and you need to add a field with depend (3,4,5) options values, then use this following way.

->addFieldDependence(
        $childFieldTwo->getName(),
        $parentField->getName(),
        array('3', '4', '5')
    )

Should be

->addFieldDependence(
        $childFieldTwo->getName(),
        $parentField->getName(),
        '3,4,5'
    )

when you select 3 or 4 or 5 then your depend field show.

Check updated code, it should work.

namespace Siarhey\Test\Block\Adminhtml\Promo\Quote\Edit\Tab;

class Actions extends \Magento\Backend\Block\Widget\Form\Generic implements
    \Magento\Backend\Block\Widget\Tab\TabInterface
{
/**
     * @param \Magento\Backend\Block\Template\Context $context
     * @param \Magento\Framework\Registry $registry
     * @param \Magento\Framework\Data\FormFactory $formFactory
     * @param array $data
     */
    public function __construct(
        \Magento\Backend\Block\Template\Context $context,
        \Magento\Framework\Registry $registry,
        \Magento\Framework\Data\FormFactory $formFactory,
        array $data = []
    ) {
        parent::__construct($context, $registry, $formFactory, $data);
    }

    public function getTabLabel()
    {
        return __('Actions');
    }

    public function getTabTitle()
    {
        return __('Actions');
    }

    public function canShowTab()
    {
        return true;
    }

    public function isHidden()
    {
        return false;
    }

    protected function _prepareForm()
    {
        $model = $this->_coreRegistry->registry('current_promo_quote_rule');

        /** @var \Magento\Framework\Data\Form $form */
        $form = $this->_formFactory->create();
        $form->setHtmlIdPrefix('rule_');

        $fieldset = $form->addFieldset(
            'action_fieldset',
            ['legend' => __('Rules')]
        );

        $parentField = $fieldset->addField(
            'simple_action',
            'select',
            [
                'label' => __('Apply'),
                'name' => 'simple_action',
                'options' => [
                    1 => __('Amount 1'),
                    2 => __('Discount 1'),
                    3 => __('Amount 2'),
                    4 => __('Discount 2'),
                ]
            ]
        );

        $childFieldOne = $fieldset->addField(
            'amount',
            'text',
            [
                'name' => 'amount',
                'required' => true,
                'class' => 'validate-not-negative-number',
                'label' => __('Amount')
            ]
        );
        //$model->setAmount($model->getAmount() * 1);

        $childFieldTwo = $fieldset->addField(
            'percent',
            'text',
            ['name' => 'percent', 'label' => __('Percent')]
        );
        //$model->setPercent($model->getPercent() * 1);

        $this->setChild(
            'form_after',
            $this->getLayout()->createBlock(
                'Magento\Backend\Block\Widget\Form\Element\Dependence'
            )->addFieldMap(
                $parentField->getHtmlId(),
                $parentField->getName()
            )->addFieldMap(
                $childFieldOne->getHtmlId(), 
                $childFieldOne->getName()
            )->addFieldMap(
                $childFieldTwo->getHtmlId(), 
                $childFieldTwo->getName()
            )->addFieldDependence(
                $childFieldOne->getName(),
                $parentField->getName(),
                '1,3'
            )->addFieldDependence(
                $childFieldTwo->getName(),
                $parentField->getName(),
                '2,4'
            )
        );

        //$form->setValues($model->getData());

        /*if ($model->isReadonly()) {
            foreach ($fieldset->getElements() as $element) {
                $element->setReadonly(true, true);
            }
        }*/

        $this->setForm($form);
        return parent::_prepareForm();
    }
}