
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 an ellipse $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) with an eccentricity of $e$, and the sum of the distances from any point on the ellipse $C$ to the two foci of the ellipse $C$ is 6.

(1) Find the equation of the ellipse $C$;

(2) Let line $l$: $y = kx - 2$ intersect the ellipse $C$ at points $A$, $B$, and let point $P(0,1)$, with $|PA| = |PB|$, find the equation of line $l$.

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