
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
We have a standard deck of 52 cards, with 4 cards in each of 13 ranks. We call a 7-card poker hand a "full house plus two" if the hand has 3 cards of one rank, 2 cards of another rank, and each of the remaining two cards from different ranks (such as 333557K). What is the probability that seven cards chosen at random form a "full house plus two"?

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