
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
A sports club has launched an activity where customers who spend money at the club have a chance to participate in a lucky draw. The club places three balls labeled with the letters $A$, $B$, and $C$ respectively, in an opaque box. Each ball is identical except for the letter on it. After mixing the balls, a customer randomly picks one ball from the box, notes the letter on it, and then returns it. The customer can exchange the letter for a sports experience voucher ($A$: table tennis; $B$: badminton; $C$: swimming). Xiao Ming and Xiao Liang each participate in the lucky draw once. Using a tree diagram (or list) method, find the probability that both Xiao Ming and Xiao Liang draw a voucher for a ball sport.

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