
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
Suppose that $\{a_n\}$ is a geometric sequence with a common ratio $q=2$, and $S_n$ is the sum of the first $n$ terms of $\{a_n\}$. Let $T_n = \frac{17S_n - S_{2n}}{a_{n+1}}$, where $n \in \mathbb{N}^*$. If $T_n$ is the maximum term of the sequence $\{T_n\}$, then find the value of $n$.

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