
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 6-card poker hand a "full house plus" if the hand contains a full house (3 cards of one rank and 2 cards of another rank) plus an additional card that does not form another pair or a four of a kind in combination with the full house. What is the probability that six cards chosen at random form this specific type of hand?

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