
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, each of distinct weight from one another and from seven genuine coins, are included in a set of 10 coins. A pair of coins is randomly selected without replacement from the 10 coins, then a second pair is selected from the remaining 8 coins. If the total weight of the first pair equals the total weight of the second pair, determine the probability that all four selected coins are genuine.

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