
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 team of 6 people checks into a hotel with 6 rooms, where room numbers 301 and 302 are opposite each other, as are 303 and 304, and 305 and 306. If each person randomly picks one of the 6 room keys, the probability that persons A and B end up with rooms directly opposite each other is ______.

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