
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 bag contains 8 green marbles, 12 purple marbles, and 5 orange marbles. Four marbles are selected at random and without replacement. What is the probability that exactly two of the marbles are purple and two are orange?

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