
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 the sequence $\{a\_n\}$ that satisfies $2a_{n+1}=a_{n}+a_{n+2}$ for all positive integers $n$, and its first $n$ terms sum $S_{n}$. It is known that $a_{5}=5$ and $S_{7}=28$.
(I) Find the sum $T_{n}$ of the first $n$ terms of the sequence $\{\frac{1}{S_{n}}\}$.
(II) If the sequence $\{b_{n}\}$ satisfies $b_{1}=1$ and $b_{n+1}=b_{n}+q^{a_{n}}$ where $q > 0$, find the general term formula for $\{b_{n}\}$.

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