
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 heavier than the genuine coins, are mixed with 9 identical genuine coins. A set of three coins is selected at random without replacement from the 12 coins. A second set of three coins is selected at random without replacement from the remaining 9 coins. The combined weight of the first set is equal to the combined weight of the second set. Calculate the probability that all 6 selected coins are genuine.

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