
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
In the sequence $\left\{a_{n}\right\}$, if $a_{i}+a_{i+1}+a_{i+2}$ is odd, then $\left(a_{i}, a_{i+1}, a_{i+2}\right)$ is called a "great triplet". For example, in the sequence $6, 4, 2, 1, 3, 5$, there are exactly two great triplets: $(4,2,1)$ and $(1,3,5)$. If $a_{1}, a_{2}, \cdots, a_{2021}$ is a permutation of $1, 2, \cdots, 2021$, determine the maximum number of great triplets in the sequence $a_{1}, a_{2}, \cdots, a_{2021}$.

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