
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 geometric sequence $\{a_{n}\}$, it is known that $a_{2}=2$ and $a_{5}=16$.
(1) Find the general term $a_{n}$ of the sequence.
(2) If the arithmetic sequence $\{b_{n}\}$ satisfies $b_{1}=a_{5}$ and $b_{8}=a_{2}$, find the sum $S_{n}$ of the first $n$ terms of $\{b_{n}\}$, and find the maximum value of $S_{n}$.

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