
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
Consider a standard deck of 52 cards with 4 cards in each of 13 ranks. We define a 6-card poker hand as having exactly three pairs (such as 334455 or QQKKAA). What is the probability that six cards chosen at random form a hand with exactly three pairs?

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