
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 sequence $\{a\_n\}$ that satisfies $a\_2=3$ and $a\_5-2a\_3+1=0$.

(1) Find the general term formula for $\{a\_n\}$.
(2) If sequence $\{b\_n\}$ satisfies $\{b\_n\}=(-1)^{n}a\_n+n (n∈ℕ^{∗})$, find the sum of the first $n$ terms, $S\_n$, of $\{b\_n\}$.

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