
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
Solve the equation $\frac{n!}{2} = k! + l!$ in natural numbers, where $n! = 1 \cdot 2 \cdot \ldots n$. In your answer, indicate 0 if there are no solutions, $n$ if there is one solution, and the sum of values of $n$ for all solutions if there are several solutions. Note that a solution is a triple $(n, k, l)$; if solutions differ in at least one component, they are considered different.

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