
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 \(0 \leq a_{k} \leq 1 \) for \(k=1,2, \ldots, 2020\), and defining \(a_{2021} = a_{1}\), \(a_{2022} = a_{2}\), find the maximum value of \(\sum_{k=1}^{2020}\left(a_{k} - a_{k+1}a_{k+2}\right)\).

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