
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
Given that the sequence $\{a\_n\}$ is an increasing geometric sequence, and $a\_1 + a\_3 = 17$, $a\_1 a\_3 = 16$.

1. Find the general term formula of the sequence $\{a\_n\}$.
2. If $b\_n = \log_{\frac{1}{2}}a\_n + 11$, and $T\_n$ is the sum of the absolute values of the first $n$ terms of the sequence $\{b\_n\}$, find $T\_n$.

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