
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
A sequence of $0$s, $1$s, and $2$s of length $24$ that begins and ends with a $0$, contains no two consecutive $0$s or $2$s, and contains no three consecutive $1$s. Find the total number of such sequences.

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