
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 ellipse $\frac{y^{2}}{9}+x^{2}=1$, a line passes through point $P(\frac{1}{2}, \frac{1}{2})$ and intersects the ellipse at points $A$ and $B$. If the chord $AB$ is bisected by point $P$, what is the equation of line $AB$?

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