
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
The equation of an ellipse $C$ with one focus at $F_1(0,1)$ and passing through the point $P\left( \dfrac{3}{2},1\right)$ is given by $\dfrac{x^{2}}{a^2} + \dfrac{y^{2}}{b^2} = 1$. Find the equation of the ellipse.

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