
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
In a game where two players, Chris and Dana, take turns rolling a standard die. If a player rolls \(n\), she is awarded \(f(n)\) points, where
\[
f(n) = \left\{
\begin{array}{cl}
8 & \text{ if } n \text{ is a multiple of 3 but not 2}, \\
3 & \text{ if } n \text{ is a multiple of 2 but not 3}, \\
0 & \text{ if } n \text{ does not satisfy either condition}.
\end{array}
\right.
\]
Chris rolls the die four times and gets 5, 2, 1, and 6. Dana rolls and gets 6, 2, 3, and 3. How many points in total does Dana earn, and what is the product of Chris's total points and Dana's total points?

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