
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
In a "6 out of 45" lottery ticket, there are 45 natural numbers. Each participant in the lottery must choose a combination of exactly 6 numbers from these 45. Two participants independently choose their combinations. What is the probability that there will be exactly one common number in their combinations?

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