
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 $y$ satisfy the equation $x^{2}+y^{2}-4x+1=0$.
$(1)$ Find the maximum and minimum values of $\dfrac {y}{x}$;
$(2)$ Find the maximum and minimum values of $y-x$;
$(3)$ Find the maximum and minimum values of $x^{2}+y^{2}$.

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