
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
The sequence \( \{a_n\} \) satisfies \( a_{n+1} = (-1)^n n - a_n \) for \( n = 1, 2, 3, \ldots \), and \( a_{10} = a_1 \). Find the maximum value of \( a_n a_{n+1} \).

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