
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 in the geometric sequence $\{a_n\}$, all terms are positive, and it is known that $a_2=2$, $a_3 \cdot a_5=64$,

(1) Find the general formula for the sequence $\{a_n\}$;

(2) Let $b_n=\log_2 a_n$, find the sum of the first $n$ terms of the sequence $\{a_{n+1} \cdot b_{n+1}\}$, denoted as $T_n$.

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