
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
Given that Maria scored $5, 2, 4, 3, 6, 2, 7, 4, 1,$ and $3$ goals in her first $10$ soccer matches, her total score after $11$ matches is divisible by $11$, and her total score after $12$ matches is divisible by $12$. Find the product of the number of goals she scored in the eleventh and twelfth matches.

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