
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 $n$, she is awarded $g(n)$ points, where  
\[g(n) = \left\{
\begin{array}{cl} 
7 & \text{if } n \text{ is a multiple of 3 and 5}, \\
3 & \text{if } n \text{ is only a multiple of 3}, \\
0 & \text{if } n \text{ is not a multiple of 3}.
\end{array}
\right.\]
Charlie rolls the die four times and gets a 6, 2, 3, and 5. Dana rolls and gets 5, 3, 1, and 3. What is the product of Charlie's total points and Dana's total points?

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