
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
In the arithmetic sequence $\{a\_n\}$, let $S\_n$ denote the sum of its first $n$ terms. Given that $a\_2=2$, $S\_5=15$, and the geometric sequence $\{b\_n\}$ with a common ratio of $2$ satisfies $b\_2+b\_4=60$.
(I) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
(II) If $c\_n=\frac{2a\_n}{b\_n}$, find the sum $T\_n$ of the first $n$ terms of the sequence $\{c\_n\}$.

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