
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
Below is the graph of an ellipse situated in a coordinate plane where major and minor axes lie vertically and horizontally respectively. Endpoint of the major axis on a vertical line are at $(2, 0)$ and $(2, 8)$. Endpoint of the minor axis on a horizontal line are at $(0, 4)$ and $(4, 4)$.

Compute the coordinates of the focus of the ellipse with the greater $y$-coordinate.

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