
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
In a bag containing 12 green marbles and 8 purple marbles, Phil draws a marble at random, records its color, replaces it, and repeats this process until he has drawn 10 marbles. What is the probability that exactly five of the marbles he draws are green? Express your answer as a decimal rounded to the nearest thousandth.

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