
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
Person A and person B are trying to independently crack a code. The probability of each person succeeding is respectively $\frac{1}{3}$ and $\frac{1}{4}$. Calculate:
(1) The probability that exactly one person cracks the code;
(2) The minimum number of people with the same ability as person B required to achieve a probability of at least $\frac{99}{100}$ of cracking the code.

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