
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
Jack and Jill play a game where they alternate turns rolling a standard six-sided die. If a player rolls $m$, they are awarded $g(m)$ points, where 
\[g(m) = \left\{
\begin{array}{cl}
8 & \text{if } m \text{ is a multiple of 3}, \\
3 & \text{if } m \text{ is a prime number}, \\
1 & \text{if } m \text{ is only even}, \\
0 & \text{otherwise}.
\end{array}
\right.\]
Jack rolls the die five times and gets a sequence of 2, 5, 6, 4, 3. Jill rolls it and gets 1, 6, 3, 2, 5. Calculate the product of Jack's total points and Jill's total points.

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