
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 $q= \sqrt {2}$. 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 $n∈N^{}$, and let $B\_n$ be the maximum term of the sequence $\{T\_n\}$. Find the value of $n$.

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