
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
Cora and Dana play a game where they take turns rolling a standard die. If a player rolls $n$, she is awarded $g(n)$ points, where  
\[ g(n) = \left\{
\begin{array}{cl}
8 & \text{ if } n \text{ is a multiple of 3 and 2}, \\
4 & \text{ if } n \text{ is a multiple of 3 but not of 2}, \\
3 & \text{ if } n \text{ is only a multiple of 2}, \\
1 & \text{ if } n \text{ is not a multiple of 2 or 3}.
\end{array}
\right.\]
Cora rolls the die six times and gets the numbers 5, 4, 3, 6, 2, and 1. Dana rolls and gets the numbers 6, 3, 4, 3, 5, and 3. What is the product of Cora's total points and Dana's total points?

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