
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 \( \left( 0, 0, 11 \right) \), 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 the balls?

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