Help with Save As for Photoshop Actions?

I'm trying to solve a bit of a bottleneck issue in my process currently. I'm manually batch processing files into contact sheets for a dieline using a combination of an action and manual input.

I first open the source file. Then I run my action. My action currently runs like this:

Open Template File

Select Previous Document

Duplicate Current Layer (To Template File)

Select Next Document

Set Current Layer (to Layer 1)

Move Current Layer (aligning to document edge)

Play a secondary action that duplicates and moves the duplicate layers till they're 3 columns x 7 rows in quantity.

Flatten the image

The problem is, after that action is run, I have to manually save out the template file to match the original file's naming convention.

i.e. template file.psd > 12345_Design_Color_DL.tiff

This can take a ton of time as I have hundreds of files to run through and batch processing them afterwords isn't much of an option as there are different design names and colorways per file. My hope is that it might be possible to add to the action to do a Save As and rename the template file to the same name as the first file I open. Then I'd be able to batch process the files and have it save out a copy with an additional _DL (for dieline) added to the name and hopefully save myself hours worth of headache in making sure files are named the same.

TL:DR

I want to be able to rename an open file [template file] to the same name as another open file [source file] with an addition to the name after an action has been run. I can't seem to get my brain to wrap around the logic to make it work though. Is there any way to do this? Any help on this matter would be greatly appreciated!