
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 take turns rolling a standard die. If a player rolls $n$, she is awarded $f(n)$ points, where  \[f(n) = \left\{
\begin{array}{cl} 
12 & \text{ if }n\text{ is a multiple of 3}, \\
4 & \text{ if }n\text{ is only a multiple of 2}, \\
0 & \text{ if }n\text{ is neither a multiple of 2 nor 3}.
\end{array}
\right.\]
Allie rolls the die five times and gets a 2, 6, 3, 1, and 6. Betty rolls four times and gets a 4, 6, 3, and 5. Calculate the product of Allie's total points and Betty's total points.

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