
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 Student Union of a certain school is holding a knowledge competition titled "Celebrating the 20th National Congress and Striving for a New Journey." The competition is divided into two rounds, and each participant must take part in both rounds. If a participant wins in both rounds, they are considered to have won the competition. It is known that in the first round, the probabilities of participants A and B winning are $\frac{3}{5}$ and $\frac{3}{4}$, respectively. In the second round, the probabilities of participants A and B winning are $\frac{3}{5}$ and $\frac{1}{2}$, respectively. The outcomes of A and B winning in each round are independent of each other.

$(1)$ If one person is selected from A and B to participate in the competition, who has a higher probability of winning?

$(2)$ If both A and B participate in the competition, what is the probability that at least one of them wins?

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