
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
Three counterfeit coins of equal weight are mixed with 12 identical genuine coins. The weight of each counterfeit coin is different from the weight of each genuine coin. Two pairs of coins are selected at random without replacement from the 15 coins, first a pair of two and then another pair of two from the remaining. What is the probability that all four selected coins are genuine?

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