How to set "input/ProductCategoryInput" widget with a javascript variable

Summary:

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I have a form where I am doing some custom logic based on other fields. I need to set the "input/ProductCategoryInput" default_value programmatically with the value of a JS variable before creating the incident on form submittion.

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Code Snippet (add any code snippets that support your topic, if applicable):

<rn:widget path="input/ProductCategoryInput" id="OracleModel" name="Incident.Product" default_value= ""/>

I can provide a default_value in the widget and it works.

I know there is a way to set the value via variable / php, but due to custom coding with user interaction, I don't have the ability to make it available when the php code is run on page load.