
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 \( 0 \leqslant a_{k} \leqslant 1 \) for \( k = 1, 2, \cdots, 2002 \), and let \( a_{2003} = a_{1} \) and \( a_{2004} = a_{2} \), find the maximum value of \( \sum_{k=1}^{20002} \left( a_{k} - a_{k+1} a_{k+2} \right) \).

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