
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 radius 8, and the other centered at $(0,0,3)$ with radius 5. How many points \((x,y,z)\) with integer coordinates are there in the intersection of these two spheres?

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