
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 that the first term of a geometric sequence $\{a\_n\}$ is $\frac{3}{2}$, and the sum of the first $n$ terms is $S\_n (n∈N^*)$, and $-2S\_2$, $S\_3$, $4S\_4$ form an arithmetic sequence.

(I) Find the general term formula of the sequence $\{a\_n\}$;

(II) Let $T\_n = S\_n + \frac{1}{S\_n} (n∈N^*)$, find the maximum term of the sequence $\{T\_n\}$.

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