
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
The target consists of 3 mutually exclusive zones. With one shot at the target, the probability of hitting the first zone for this shooter is 0.5. For the second and third zones, the probabilities are 0.3 and 0.2, respectively. The shooter fires 6 shots at the target. Find the probability that there will be 3 hits in the first zone, 2 hits in the second zone, and 1 hit in the third zone.

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