
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 $\{a\_n\}$, it is known that the sum of the first 3 terms is equal to the sum of the first 10 terms, and the first term $a\_1 > 0$. $S\_n$ represents the sum of the first $n$ terms. If $S\_n$ takes the maximum value, then $n=$ \_\_\_\_\_\_.

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