
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
In a standard deck of 52 cards, each rank has 4 cards. A 5-card poker hand is considered a "special full house" if the hand has 3 cards of one rank and the remaining 2 cards are of the same suit but different ranks (e.g., 333AD, where 3s are of any suit and A and D are diamonds). What is the probability that five cards chosen at random form a "special full house"?

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