
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 and/or $1$s is randomly generated. Determine the probability that the sequence does not contain three consecutive $1$s. If this probability can be written in the form $\dfrac{p}{q}$, where $p, q$ are relatively prime positive integers, find $p+q$.

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