
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 first $n$ terms of an increasing geometric sequence ${a_n}$ sum to $S_n$, $a_6=64$, and the arithmetic mean of $a_4$ and $a_5$ is $3a_3$.
1. Find the general term formula for ${a_n}$.
2. Let $b_n=\frac{n}{a_{2n-1}}$, 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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