
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
Alice, Bob, and Charlie each pick a 2-digit number at random. What is the probability that all of their numbers' tens digits are different from each other's tens digits and all of their numbers' ones digits are different from each other's ones digits?

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