
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 a sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$. The sequence satisfies the conditions $a\_1=23$, $a\_2=-9$, and $a_{n+2}=a\_n+6\times(-1)^{n+1}-2$ for all $n \in \mathbb{N}^*$.
(1) Find the general formula for the terms of the sequence $\{a\_n\}$;
(2) Find the value of $n$ when $S\_n$ reaches its maximum.

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