
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
The sequence $\{a_n\}$ satisfies: $a_n = 13 - 3n$, and $b_n = a_n \cdot a_{n+1} \cdot a_{n+2}$. Let $S_n$ be the sum of the first $n$ terms of $\{b_n\}$. Calculate the maximum value of $S_n$.

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