
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
From a standard deck of 52 cards, calculate the probability of drawing a 5-card hand that consists of "three of a kind" where exactly 3 cards are of one rank and the other 2 cards are each of different ranks from each other and from the triple.

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