
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
Charlie and Dana play a game where they take turns rolling a standard die. If a player rolls $n$, they are awarded $g(n)$ points, where:
\[g(n) = \left\{
\begin{array}{cl}
8 & \text{if }n\text{ is a multiple of 3}, \\
3 & \text{if }n\text{ is a prime number}, \\
1 & \text{if }n\text{ is only even (and not a multiple of 3)},
\\ 0 & \text{otherwise}.
\end{array}
\right.\]
Charlie rolls the die five times and gets the numbers 6, 4, 5, 2, and 3. Dana rolls the die four times and gets the numbers 3, 3, 1, and 2. Calculate the product of Charlie's and Dana's total points.

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