
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 the two-dimensional Cartesian coordinate system, the equation of a circle with center at point $({x_0}, {y_0})$ and radius $r$ is $({x-{x_0})^{2}}+({y-{y_0})^{2}}={r^{2}}$. By analogy with the circle's equation, write the equation of a sphere in the three-dimensional Cartesian coordinate system with center at point $P({x_0}, {y_0}, {z_0})$ and radius $r$.

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