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

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