
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 $\{a_n\}$ is an arithmetic sequence, and the sequence $\{b_n\}$ satisfies $b_n = a_na_{n+1}a_{n+2} (n \in \mathbb{N}^*)$. Let $S_n$ be the sum of the first $n$ terms of $\{b_n\}$. If $a_{12} = \frac{3}{8}a_5 > 0$, then when $S_n$ reaches its maximum value, the value of $n$ is equal to .

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