
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 that there are sequences of 0's and 1's of length 15 that begin with a 0, end with a 0, contain no two consecutive 0's, and contain no three consecutive 1's, calculate the total number of such sequences.

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