
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 fifty-two cards consists of four $1$'s, four $2$'s,..., and four $13$'s. A matching pair (two cards with the same number) and one single card of a different number are removed from the deck. Given that these cards are not returned to the deck, let $m/n$ be the probability that three randomly selected cards from the remaining deck consists of three cards with the same number, 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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