
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
There are two boxes, box A and box B, each containing four balls labeled $1$, $2$, $3$, and $4$. One ball is drawn from each box, with each ball having an equal chance of being selected.
(I) Find the probability that the numbers on the two drawn balls are the same.
(II) Find the probability that the product of the numbers on the two drawn balls is divisible by $3$.

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