
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 standard deck of fifty-two cards consists of four cards of each rank from Ace through King. Two matching pairs are removed from the deck (two pair of Aces and two pairs of Kings). Calculate the probability that two randomly selected cards from the remaining deck also form a pair, and express the result in the simplified form \( m/n \) where \( m \) and \( n \) are relatively prime positive integers. Find \( m + n \).

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