
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 sequence $\{a\_n\}$ with a common ratio $q > 1$, the sum of the first $n$ terms is $S\_n$. It is known that $S\_3=7$ and the sequence $a\_1+3$, $3a\_2$, $a\_3+4$ forms an arithmetic sequence.

(I) Find the general term formula for the sequence $\{a\_n\}$;
(II) Let $c\_n=(3n-2)a\_n$, find the sum of the first $n$ terms, $T\_n$, for the sequence $\{c\_n\}$.

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