
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
Suppose there are 3 counterfeit coins of equal weight mixed with 12 genuine coins. All counterfeit coins weigh differently from the genuine coins. A pair of coins is selected at random without replacement from the 15 coins, followed by selecting a second pair from the remaining 13 coins. The combined weight of the first pair equals the combined weight of the second pair. What is the probability that all four coins selected are genuine?
A) $\frac{7}{11}$
B) $\frac{9}{13}$
C) $\frac{11}{15}$
D) $\frac{15}{19}$
E) $\frac{15}{16}$

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