
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 shooter fires once with a probability of 0.8 to hit the target. He shoots 5 times in a row, and the outcomes of these shots are independent of each other. Calculate (results should be rounded to the second decimal place):
(1) The probability of hitting the target exactly 2 times out of 5 shots;
(2) The probability of hitting the target at least 2 times out of 5 shots;
(3) The probability of hitting the target exactly 2 times out of 5 shots, and the third shot is a hit.

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