
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
Find all sequences  $\left(a_0,a_1,a_2,a_3\right)$ , where for each  $k$ ,  $0\leq k\leq3$ ,  $a_k$  is the number of times that the number  $k$  appears in the sequence  $\left(a_0,a_1,a_2,a_3\right)$ .

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