
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
Inside the circle $x^2+y^2=8$, there is a point $P_0(-1, 2)$. $AB$ is a chord passing through point $P_0$ with an inclination angle of $\alpha$;  
(1) When $\alpha= \frac {3\pi}{4}$, find the length of chord $AB$;  
(2) When chord $AB$ is bisected by point $P_0$, find the equation of line $AB$.

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