
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 $a_1 + a_3 = 17$, $a_1a_3 = 16$  
(1) Find the general formula for 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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