
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 equation of an ellipse: $\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1$, and a point $P$ with coordinates $(1, \frac{3}{2})$. A line $l$ that does not pass through point $P$ has the equation $y = kx + b$ and intersects the ellipse at points $A$ and $B$. If $PA \perp PB$ and $AB$ is bisected by the $y$-axis, find the equation of line $l$.

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