
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
A sphere with radius 2 and center at $(0,0,2)$ is resting on the $xy$-plane. A light source is located at $(0, -2, 3)$. Determine the boundary of the shadow of the sphere on the $xy$-plane, which can be described by a function $y = g(x)$.

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