
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 $\{a\_n\}$,

1. Given $a\_4=10$, $a\_{10}=-2$, and $S\_n=60$, find $n$.
2. Given $a\_1=-7$, $a\_n+1=a\_n+2$, find $S\_17$.
3. If $a\_2+a\_7+a\_12=24$, find $S\_13$.

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