
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 \( a_{0} = 0 \), \( a_{1} = a_{2} = 1 \), \( a_{3n} = a_{n} \), and \( a_{3n+1} = a_{3n+2} = a_{n}+1 \) for \( n \geq 1 \), find the value of \( a_{2021} \).

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