
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 Lucas's first $10$ football matches, he scored the following points: $5, 2, 6, 3, 10, 1, 3, 3, 4, 2$. For his next two games, he maintained his scoring to be fewer than $10$ points each, and he wants each overall match average up to and including each game to be an integer. What is the product of the number of points he scored in the eleventh and twelfth games?
A) 10
B) 20
C) 30
D) 40
E) 50

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