
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 the sequence of $0$s and $1$s of length $23$, and the conditions that it begins with a $0$, ends with a $0$, contains no two consecutive $0$s, and contains no four consecutive $1$s, determine the number of such sequences.

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