
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 an expanded deck of 56 cards, with 4 cards in each of 14 ranks. We call a 5-card poker hand a full house if the hand has 3 cards of one rank and 2 cards of another rank. What is the probability that five cards chosen at random from this expanded deck form a full house?

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