
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
Chris and Paul each rent a different room of a hotel from rooms 1 to 60. The hotel manager mistakes them for one person and assigns them a room number formed by concatenating Chris's and Paul's room numbers. For example, if Chris has room 15 and Paul has room 9, their concatenated room number would be 159. If there are 360 rooms in the hotel, what is the probability that the concatenated room number is a valid room number within the range 1 to 360?

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