
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given $m$ and $n$ are positive integers with $m > n > 4$, and the decimal representation of $m!$ ends in $k$ zeros and the decimal representation of $(m+n)!$ ends in $2k$ zeros, find the sum of the digits of the sum of the three least possible values of $m$ for which $n=6$.

Present the answer in LaTex format: \boxed{Your answer}
user