Injecting values into parent theme (add value to form action="{$my_value}"

I want to add a value to action on the account template so that where it says <form action=”<?php echo $my_value; ?>”>

Now I know this is possible to do if i copy the whole template into my child theme and add the value. However, the account template is huge and I don’t want to copy the whole thing just for one line of code.

What would be the best way to add this code, could it be done with a plugin?
Can it be done with a function?
Or is the only way simply to copy it?