
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 $\left(0, 0, 10\right)$ with a radius of 5, and the other centered at $(0,0,4)$ with a radius of 6. Determine how many points $(x, y, z)$ with integer coordinates are there in the intersection of the balls.

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