
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
In the geometric sequence $\{a\_n\}$, the common ratio $q > 0$, and $S\_n$ denotes the sum of its first $n$ terms. Given that $S\_2=3$ and $S\_4=15$, find:
1. $a\_n$;
2. Let $T\_n$ be the sum of the first $n$ terms of the sequence $\{S\_n\}$, find $T\_n$.

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