
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
Given Professor Smart selects six distinct integers from 1 to 60 such that the product of these integers is a power of 10, and the sum of these integers is divisible by 11, calculate the probability that Professor Smart's selection matches the winning ticket also having these properties.

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