
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 students, A and B, participate in a three-point basketball shooting competition. The probability of A making a shot is $\frac{1}{3}$, while the probability of B making a shot is $\frac{1}{2}$. Each of them attempts three shots.

1. Find the probability that B makes at most 2 shots.
2. Find the probability that B makes exactly 2 more shots than A.

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