
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 its first $n$ terms is $S_n$ $(n \in \mathbb{N^*})$, and $-2S_2, S_3, 4S_4$ form an arithmetic sequence.

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

(II) Find the maximum and minimum values of $S_n$ $(n \in \mathbb{N^*})$.

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