
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
Let $\{a\_n\}$ be a geometric sequence with a common ratio greater than $1$. $S\_n$ represents the sum of its first $n$ terms. Given that $S\_3=7$, $a\_1+3$, $3a\_2$, $a\_3+4$ form an arithmetic sequence.

(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) Let $b\_n=a\_n+\ln a\_n$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $T\_n$.

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