
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 Marco's first $6$ soccer games, he scored $2, 5, 1, 4, 6,$ and $3$ goals. In his seventh game, he scored fewer than $10$ goals, and his goals-per-game average for these $7$ games was an integer. In his eighth game, he also scored fewer than $10$ goals and the goals-per-game average for the $8$ games became an integer too. Find the product of the number of goals he scored in the seventh and eighth games.

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