
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 sequences of 0s and 1s of length 20 that begin with a 0, end with a 0, contain no two consecutive 0s, contain no three consecutive 1s, and have exactly one instance of two consecutive 1s, calculate the number of possible sequences.

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