
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
Ana and Banana are rolling a standard six-sided die. Ana rolls the die twice, obtaining \(a_1\) and \(a_2\), then Banana rolls the die twice, obtaining \(b_1\) and \(b_2\). After Ana's two rolls but before Banana's two rolls, they compute the probability \(p\) that \(a_1 b_1 + a_2 b_2\) will be a multiple of 6. What is the probability that \(p = \frac{1}{6}\)?

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