
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 0s and 1s has a length of 22 and begins and ends with 0, contains no two consecutive 0s, and contains exactly one occurrence of three consecutive 1s, calculate the number of such sequences.

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