
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
Given real numbers $x$ and $y$ satisfying the equation $(x-3)^{2}+(y-3)^{2}=6$, find  
$(I)$ The maximum and minimum values of $\frac {y}{x}$;  
$(II)$ The maximum and minimum values of $\sqrt {(x-2)^{2}+y^{2}}$.

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