
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 that $\left\{a_{n}\right\} $ is an arithmetic sequence, $(a_{3}=7 ), $ $(a_{1}+a_{7}=10 ), $ $(S_{n} )$ represents the sum of its first $n$ terms. Determine the value of $n$ that makes $(S_{n} )$ reach its maximum value.

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