
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 people are shooting, with person A having a probability of hitting the target once at $\frac{1}{2}$, and person B having a probability of hitting the target once at $\frac{1}{3}$.

(1) If each person shoots once, and hitting the target at least once is considered achieving the goal, what is the probability of achieving the goal?

(2) If each person shoots twice, and hitting the target at least three times is considered achieving the goal, what is the probability of achieving the goal?

(3) If each person shoots five times, can it be confidently asserted (with 99% certainty) that they will hit the target at least once?

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