
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 an arithmetic-geometric sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, and $S\_3=7$, $S\_6=63$.

(1) Find the expression for $a\_n$ and $S\_n$;

(2) Denote the sum of the first $n$ terms of the sequence $\{S\_n\}$ as $T\_n$, find the expression for $T\_n$.

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