
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
Let  $n$  be a positive integer. 
Determine the number of sequences  $a_0, a_1, \ldots, a_n$  with terms in the set  $\{0,1,2,3\}$  such that   $$ n=a_0+2a_1+2^2a_2+\ldots+2^na_n. $$  

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