
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  
\[f(n) = \left\{
\begin{array}{cl} 
7 & \text{ if } n \text{ is a multiple of 2 and 3}, \\
3 & \text{ if } n \text{ is only a multiple of 2}, \\
5 & \text{ if } n \text{ is prime}, \\
0 & \text{ otherwise}.
\end{array}
\right.\]
Allie rolls the die five times and gets a 2, 3, 4, 5, and 6. Betty rolls and gets 6, 3, 4, 2, and 1. What is the product of Allie's total points and Betty's total points?

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