
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 each roll a standard die five times. The points a player scores for rolling $n$ are given by: 
\[ f(n) = \left\{
\begin{array}{cl}
5 & \text{ if } n \text{ is a multiple of 3}, \\
3 & \text{ if } n \text{ is only a multiple of 2}, \\
0 & \text{ if } n \text{ is neither multiple of 2 nor 3}.
\end{array}
\right.\]
Allie's rolls are 3, 5, 6, 2, and 4. Betty's rolls are 3, 2, 1, 6, and 4. Compute the product of Allie's total points and Betty's total points.

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