
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, where it is assumed that tick marks are placed every $1$ unit along the axes.
[asy]
size(8cm);

int x, y;
for (y = -5; y <= 3; ++y) {
  draw((-1,y)--(9,y),gray(0.7));
}
for (x = -1; x <= 9; ++x) {
  draw((x,-5)--(x,3),gray(0.7));
}

draw(shift((4,-2))*xscale(2)*shift((-4,2))*Circle((4,-2),3));
draw((-1,0)--(9,0),EndArrow);
draw((0,-5)--(0,3),EndArrow);
[/asy]
Compute the coordinates of the focus of the ellipse with the greater $x$-coordinate.

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