
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 the parabola $C$: $y^{2}=-2px$ passes through point $A(-1,-2)$.

(1) Find the equation of the parabola $C$ and its axis of symmetry;

(2) A line with a slope of ${-}\sqrt{3}$ passes through the focus of the parabola, intersecting the parabola at points $A$ and $B$. Find the length of the line segment $AB$.

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