
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
We define a sequence of natural numbers by the initial values  $a_0 = a_1 = a_2 = 1$  and the recursion   $$  a_n = \bigg \lfloor \frac{n}{a_{n-1}a_{n-2}a_{n-3}} \bigg \rfloor  $$   
for all  $n \ge 3$ . Find the value of  $a_{2022}$ .

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