
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 10 counterfeit coins of equal weight and 20 identical genuine coins, if two pairs of coins are selected at random without replacement from the 30 coins, and the combined weight of the first pair is equal to the combined 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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