
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
Let us denote the product of all natural numbers from 1 to $m$ by $m!$, i.e., $m! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot (m-1) \cdot m$. Find all values of $m$ for which the sum $1! + 2! + 3! + \ldots + m!$ is a perfect square.

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