
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
Let O be the origin of coordinates, C be the center of the circle $(x-2)^2+y^2=3$, and there is a point M$(x,y)$ on the circle satisfying $\overrightarrow{OM} \cdot \overrightarrow{CM} = 0$. Solve for the value of $\frac{y}{x}$.

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