
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
Let the arithmetic sequence \( \left\{a_{n}\right\} \) have the sum of the first \( n \) terms denoted by \( S_{n} \). Given that \( S_{6}=26 \) and \( a_{7}=2 \), find the maximum value of \( n S_{n} \).

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