
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 a circle $x^{2}+y^{2}=9$, $AB$ is a chord passing through point $P(2,\sqrt{3})$ with an inclination angle of $\alpha$. <br/>$(1)$ When $\alpha =120^{\circ}$, find the length of chord $AB$; <br/>$(2)$ If chord $AB$ is bisected by point $P$, find the equation of line $AB$.

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