
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 non-negative real numbers \(a_1, a_2, \ldots, a_{100}\) satisfy: \( a_i + a_{i+1} + a_{i+2} \leq 1 \) for \( 1 \leq i \leq 100 \), where \(a_{101} = a_1\) and \(a_{102} = a_2\). Find the maximum value of \(\sum_{i=1}^{100} a_i a_{i+2}\).

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