
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 there are 23 positions in a sequence that start with 0, end with 0, and contain no two consecutive 0s and no four consecutive 1s, calculate the number of valid sequences that can be constructed.

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