
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 $\{a\_n\}$ is a geometric sequence with positive terms, and $a\_1+a\_2=6$, $a\_1a\_2=a\_3$.
(1) Find the general term formula for $\{a\_n\}$;
(2) Let $\{b\_n\}$ be an arithmetic sequence with non-zero terms and its sum of the first $n$ terms be $S\_n$. If $S\_2n+1=b\_n b\_n+1$, find the sum of the first $n$ terms of the sequence $\{\frac{b\_n}{a\_n}\}$, denoted as $T\_n$.

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