
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
Consider two solid spherical balls, one centered at $(0, 0, 10)$ with radius 8, and the other centered at $(0, 0, 2)$ with radius $6$. How many points $(x, y, z)$ with only integer coefficients are there in the intersection of these balls?

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