
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
A box contains $12$ red candies and $8$ green candies. Alice picks three candies at random, then Bob picks three of the remaining candies at random. Calculate the probability that they pick the same number of candies of each color.

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