
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 \[f(n) = \left\{
\begin{array}{cl}
9 & \text{ if } n \text{ is a multiple of 3}, \\
3 & \text{ if } n \text{ is only a multiple of 2}, \\
1 & \text{ otherwise.}
\end{array}
\right.\] This time, Allie rolls the die three times, getting a 6, 3, and 4. Betty rolls the die four times, getting 1, 2, 5, and 6. Calculate 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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