
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 the sequence $\{a\_n\}$ with the sum of its first $n$ terms $S\_n=n^2$, where $(n∈N^∗)$.
(1) Find the general term formula for the sequence $\{a\_n\}$;
(2) If the sequence $\{b\_n\}$ is a geometric sequence with common ratio $q (q>0)$, and $b\_1=S\_1$, $b\_4=a\_2+a\_3$, find the sum of the first $n$ terms $T\_n$ for the sequence $\{b\_n\}$.

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