
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 John's first $6$ basketball games, he scored $10, 5, 8, 6, 11,$ and $4$ points. In his seventh game, he scored fewer than $15$ points and his points-per-game average for the seven games was an integer. For the eighth game, he also scored fewer than $15$ points, and the average for the $8$ games became an integer again. Determine the product of the number of points he scored in the seventh and eighth games.

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