
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
Allie and Betty play a game where they alternately roll a standard die. The scoring function $g(n)$ awards points as per the following criteria:
\[g(n) = \left\{
\begin{array}{cl}
6 & \text{if } n \text{ is a multiple of 2 and 3}, \\
3 & \text{if } n \text{ is a multiple of 3 but not 2}, \\
2 & \text{if } n \text{ is a multiple of 2 but not 3}, \\
0 & \text{otherwise}.
\end{array}
\right.\]
Allie rolls the die four times, receiving the outcomes 6, 3, 2, and 4. Betty rolls the die four times as well, getting 5, 2, 3, and 6. Calculate the product of Allie's total points and Betty's total points.

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