
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
Let $\{a_n\}$ be a geometric sequence with a common ratio $q = \sqrt{2}$. Let $S_n$ denote the sum of the first $n$ terms of $\{a_n\}$. Define $T_n = \frac{17S_n - S_{2n}}{a_{n+1}}$, where $n \in \mathbb{N}^*$. Let $B_n$ be the maximum term of the sequence $\{T_n\}$. Find the value of $n$ for which $B_n$ is maximum.

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