
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
Nine people sit in three rows of three chairs each. The probability that two of them, Celery and Drum, sit next to each other in the same row is  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ . Find  $100m+n$ .

*Proposed by Michael Tang*

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