
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, and let $S_n$ be the sum of its first $n$ terms. Given that $S_3 = 7$, the sequence formed by $a_1+3$, $3a_2$, and $a_3+4$ is an arithmetic sequence.

(I) Find the general term formula for the sequence $\{a_n\}$.

(II) Define $b_n = a_n + \ln(a_n)$, calculate the sum of the first $n$ terms $T_n$ of the sequence $\{b_n\}$.

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