
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 a geometric sequence $\{a_n\}$ with the first term $\frac{3}{2}$ and the sum of the first $n$ terms denoted as $S_n$ ($n\in\mathbb{N}^*$), and $-2S_2$, $S_3$, $4S_4$ form an arithmetic sequence.  
(Ⅰ) Find the general formula for the sequence $\{a_n\}$.  
(Ⅱ) Let $T_n = S_n + \frac{1}{S_n}$ ($n\in\mathbb{N}^*$), find the maximum term of the sequence $\{T_n\}$.

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