
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 ten $0$s, $1$s, and/or $2$s is randomly generated. Each number can appear, but the sequence must not contain consecutive numbers greater than $0$. If the probability that the sequence meets this condition can be written in the form $\dfrac{m}{n}$, where $m, n$ are relatively prime positive integers, find $m+n$.

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