
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 twelve $0$s, $1$s, and/or $2$s is randomly generated with the condition that no two consecutive characters are the same. If the probability that the generated sequence meets this condition can be expressed as $\frac{m}{n}$, where $m, n$ are relatively prime positive integers, find $m+n$.

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