
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 that an ellipse passes through points $P(1, \frac{\sqrt{3}}{2})$ and $Q(2, 0)$, determine the equation of the ellipse.

A) $\frac{x^{2}}{4} + \frac{y^{2}}{2} = 1$
B) $\frac{x^{2}}{4} + y^{2} = 1$
C) $\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1$
D) $\frac{y^{2}}{4} + x^{2} = 1$

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