
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 an arithmetic-geometric sequence $\{a\_n\}$, let $S\_n$ denote the sum of its first $n$ terms. Given that $a\_1 + a\_3 = 5$, $S\_4 = 15$,

(I) Find the general term formula for the sequence $\{a\_n\}$.

(II) Let $b\_n = \frac{5}{2} \log\_2 a\_n$. Find the value of the sum of the first $n$ terms of $\{b\_n\}$, denoted by $T\_n$.

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