
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
Given that eight counterfeit coins of equal weight are mixed with 12 identical genuine coins, the weight of each of the counterfeit coins is different from the weight of each of the genuine coins. A pair of coins is selected at random without replacement from the 20 coins, and a second pair is selected at random without replacement from the remaining 18 coins. The combined weight of the first pair is equal to the combined weight of the second pair. Determine the probability that all 4 selected coins are genuine.

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