
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 eccentricity of the ellipse $C: \frac{x^2}{4} + \frac{y^2}{3} = 1$ is ______, and ellipse $C_1$ has its foci on the x-axis and shares the same eccentricity as $C$ and passes through the point $(2, -\sqrt{3})$. The standard equation of the ellipse $C_1$ is ______.

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