
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
In a jar, there are twelve balls numbered from 1 to 12. Samuel removes one ball randomly. Then, Clara removes another ball randomly. The task is to determine the probability that the product of the two numbers on the balls removed is a multiple of four.
A) $\frac{13}{44}$
B) $\frac{1}{3}$
C) $\frac{12}{29}$
D) $\frac{11}{39}$
E) $\frac{14}{41}$

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