Formula Creation for Detecting Wrong Serial Numbers in Google Sheets

Objective:
To create a formula in Google Sheets that detects instances of wrong serial numbers within file number groups and flags them accordingly.

We have Columns:

Column A: File numbers
Column X: Serial numbers
Column AM: Flag for new file number start (Output: "True" if a new file number starts, otherwise blank)

What I need is a formula to do this in:
Column AN: Flag for wrong serial numbers (Output: "False" if a wrong serial number is detected, otherwise blank)

Logic:

Check for New File Number (Column AM):

If a new file number starts in a row, the corresponding cell in column AM should output "True".
Check for Wrong Serial Numbers (Column AN):

We need formula for this: For rows within the same file number group:
If the current serial number is 1 or less than or equal to the maximum serial number in the preceding rows of the same file number group, the cell in column AN should output "False" to indicate a wrong serial number.
Otherwise, the cell in column AN should remain blank.

Deadline:
Can someone do this in few minutes and give results?

How to Apply:
Include the phrase "Excel Serial Number Guru" at the beginning of your proposal to demonstrate that you have read the job description.