
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
Gina and Helen play a game where they take turns rolling a standard die. If a player rolls \( n \), she is awarded \( g(n) \) points, where  
\[ g(n) = \left\{
\begin{array}{cl} 
8 & \text{ if } n \text{ is a multiple of 3}, \\
3 & \text{ if } n \text{ is only a multiple of 2}, \\
0 & \text{ if } n \text{ is neither a multiple of 2 nor 3}.
\end{array}
\right. \]
Gina rolls the die five times and gets the sequence 6, 5, 2, 3, and 4. Helen rolls the die five times and gets the sequence 1, 2, 4, 6, and 3. Calculate the total sum of Gina and Helen's points.

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