
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
For the ellipse $C: \frac{x^2}{4} + \frac{y^2}{3} = 1$, the length of the major axis of ellipse $C$ is ______; if the foci of ellipse $C_1$ are on the $x$-axis and it has the same eccentricity as ellipse $C$, and passes through the point $(2, -\sqrt{3})$, then the standard equation of ellipse $C_1$ is ______.

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