
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 four terms of a geometric sequence $\{a\_n\}$ have a sum of $S\_4=5$, and $4a\_1,\;\; \frac {3}{2}a\_2\;,\;a\_2$ form an arithmetic sequence.
(I) Find the general term formula for $\{a\_n\}$;
(II) Let $\{b\_n\}$ be an arithmetic sequence with first term $2$ and common difference $-a\_1$. Its first $n$ terms' sum is $T\_n$. Find the maximum positive integer $n$ that satisfies $T_{n-1} > 0$.

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