
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 the center of an ellipse is at the origin of the coordinate system, its axis of symmetry coincides with the coordinate axes, and it passes through the point $(4,0)$. The eccentricity is $\frac{\sqrt{3}}{2}$. Find the standard equation of the ellipse.

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