
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 an arithmetic sequence ${a_n}$:
(1) Given $a_4=10$, $a_{10}=-2$, and the sum of the first $n$ terms $S_n=60$, find $n$.
(2) Given $a_1=-7$ and $a_{n+1}=a_n+2$, 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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