
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 knights are seated at a round table. Five of them are randomly chosen to embark on a quest. Let $P$ be the probability that at least two of the five chosen knights are sitting next to each other. Express $P$ in the simplest fractional form and compute the sum of the numerator and denominator of $P$.

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