
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
20. It is known that a circle with center at point $P$ passes through points $A(-1,0)$ and $B(3,4)$. The perpendicular bisector of segment $AB$ intersects circle $P$ at points $C$ and $D$, and $|CD| = 4\sqrt{10}$.

(1) Find the equation of line $CD$;

(2) Find the equation of circle $P$.

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