
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
Thirty of King Arthur's knights are seated at their customary round table. Four of them are chosen - all choices being equally likely - and are sent off to slay a troublesome dragon. Let \(P\) be the probability that at least two of the four had been sitting next to each other. If \(P\) is written as a fraction in lowest terms, what is the sum of the numerator and denominator?

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