
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 deck of eighty cards includes four cards each of numbers $1$ to $20$. If three pairs—each pair consisting of two cards with the same number—are removed from distinct number sets (e.g., a pair of `7`s, a pair of `15`s, and a pair of `20`s), find the probability that two randomly selected cards from the remaining deck also form a pair. Present your answer as a sum of relatively prime integers $m + n$ where the probability is $m/n$.

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