
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
Consider the ellipse given in the equation
\[\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1.\]
The center and axes lengths are represented in the following graphical diagram:

[asy]
unitsize(0.3 cm);

int i, n = 10;

for (i = -n; i <= n; ++i) {
  draw((i,-n)--(i,n),gray(0.7));
  draw((-n,i)--(n,i),gray(0.7));
}

draw((0,-n)--(0,n));
draw((-n,0)--(n,0));

draw(shift((3,-1))*xscale(6)*yscale(4)*Circle((0,0),1),blue);

dot((3,-1));
[/asy]

Find the sum \( h + k + a + b \).

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