
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
In the increasing geometric sequence $\{a\_n\}$, $a\_1 \cdot a\_6 = 32$, $a\_2 + a\_5 = 18$, where $n \in \mathbb{N}^*$.
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) Let $b\_n = a\_n + \log\_2 a\_{n+1}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $T\_n$.

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