
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 the sequence \(\{a_n\}\) that satisfies \(a_n = n\) for \(1 \leq n \leq 5\), and \(a_{n+1} = a_1 \cdot a_2 \cdot \ldots \cdot a_n - 1\) for \(n \geq 5\), find the maximum value of \(S_m = a_1 \cdot a_2 \cdot \ldots \cdot a_m - a_1^2 - a_2^2 - \ldots - a_m^2\).

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