
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
Alex and Bob play a game where they each roll a standard die five times. Players are awarded points based on the number rolled, using the following function:
\[ f(n) = \left\{
\begin{array}{cl} 
8 & \text{ if } n \text{ is a multiple of 3}, \\
4 & \text{ if } n \text{ is a multiple of 2 but not 3}, \\
0 & \text{ otherwise}.
\end{array}
\right.\]
Alex rolls the die and gets the numbers 6, 4, 3, 2, and 1. Bob rolls the die and gets the numbers 5, 6, 2, 3, and 3. Calculate the product of Alex's total points and Bob's total points.

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