
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 eight \(0\)s and/or \(1\)s is randomly generated. If the probability that the sequence does not contain two consecutive \(1\)s 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