
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 sequence is not decreasing. The sum of the first $n$ terms is denoted as $S\_n (n∈N^{})$, and $S\_3+a\_3$, $S\_5+a\_5$, $S\_4+a\_4$ form an arithmetic sequence.

1. Find the general term formula for the sequence $\{a\_n\}$;
2. Let $T\_n=S\_n-\frac{1}{S\_n} (n∈N^{})$, find the maximum and minimum values of the sequence $\{T\_n\}$.

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