
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
Two shooters are firing at a target. The probability of a miss for each shot is 0.2 for the first shooter and 0.4 for the second shooter. Find the most likely number of volleys in which neither hitter hits the target if the shooters make 25 volleys.

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