
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
Let the geometric sequence $\{a_n\}$ consist of positive terms, and let the sequence $\{b_n\}$ satisfy $b_n = a_{2n-1} \cdot a_{2n+1}$, with $b_1 = 4$ and $b_2 = 64$.

$(1)$ Find the general term of $\{a_n\}$.

$(2)$ Find the sum of the first $n$ terms of $\{b_n\}$, denoted as $T_n$.

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