
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 an geometric sequence $\left\{ a_n \right\}$, where $2a_4-3a_3+a_2=0$ and $a_1=64$ with the common ratio $q\ne 1$,

(1) Find $a_n$;

(2) Let $b_n=\log_2{a_n}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$;

(3) Under the condition of (2), find the maximum value of $T_n$.

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