
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 hyperbola $\frac {x^{2}}{4}- \frac {y^{2}}{2}=1$, the line $l$ intersects the hyperbola at points $A$ and $B$. If the coordinates of the midpoint of segment $AB$ are $(\frac {1}{2},-1)$, find the equation of line $l$.

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