
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
To popularize knowledge about epidemic prevention and promote the spirit of epidemic prevention, a certain school organized an epidemic prevention knowledge competition. The competition is divided into two rounds, and each participant must participate 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 of the competition, the probabilities of participants A and B winning are $\frac{5}{6}$ and $\frac{3}{5}$ respectively; in the second round of the competition, the probabilities of participants A and B winning are $\frac{2}{3}$ and $\frac{3}{4}$ respectively. The outcomes of A and B winning in each round are independent of each other.<br/>$(1)$ Among participants A and B, who has a greater probability of winning the competition if one of them is selected to participate?<br/>$(2)$ If both participants A and B participate in the competition, what is the probability that at least one of them wins the competition?

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