
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. (Assume that tick marks are placed every $1$ unit along the axes.)
[asy]
size(8cm);

int x, y;
for (y = -4; y <= 2; ++y) {
  draw((-1,y)--(7,y),gray(0.7));
}
for (x = -1; x <= 11; ++x) {
  draw((x,-4)--(x,2),gray(0.7));
}

draw(shift((5,-1))*xscale(2.5)*shift((-5,1))*Circle((5,-1),3));
draw((-1,0)--(11,0),EndArrow);
draw((0,-4)--(0,2),EndArrow);

[/asy]
Compute the coordinates of the focus of the ellipse with the greater $x$-coordinate. The endpoints of the major axis of the ellipse are $(0,-1)$ and $(10,-1)$, and the endpoints of the minor axis of the ellipse are $(5,2)$ and $(5,-4)$.

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