
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
Athletes A and B are playing a shooting game. In each round, A and B each take one shot. It is known that the probability of A making a shot in a round is $\frac{4}{5}$, and the probability of B making a shot is $\frac{3}{4}$. The results of A and B making a shot in each round are independent and do not affect each other. Find:<br/>
$(1)$ The probability that both A and B make a shot in one round;<br/>
$(2)$ The probability that A and B each make $3$ shots in two rounds.

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