
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 an ellipse with its center at the origin and symmetric axes aligned with the coordinates axes. The length of the major axis is twice that of the minor axis. Additionally, point $P(4,1)$ lies on the ellipse. Determine the equation of the ellipse.

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