
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 a portion of the graph of an invertible function, \( y = f(x) \):

[asy]
import graph; size(8cm); real lsf=0.5; pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); pen ds = black; real xmin = -3.25, xmax = 3.25, ymin = -6.25, ymax = 7.25;
pen cqcqcq = rgb(0.75, 0.75, 0.75);

/* grid */ pen gs = linewidth(0.7) + cqcqcq + linetype("2 2"); real gx = 1, gy = 1;
for(real i = ceil(xmin/gx)*gx; i <= floor(xmax/gx)*gx; i += gx) draw((i, ymin)--(i, ymax), gs); for(real i = ceil(ymin/gy)*gy; i <= floor(ymax/gy)*gy; i += gy) draw((xmin, i)--(xmax, i), gs);

Label laxis; laxis.p = fontsize(10);

xaxis("", xmin, xmax, Ticks(laxis, Step = 1.0, Size = 2, NoZero), Arrows(6), above=true); yaxis("", ymin, ymax, Ticks(laxis, Step = 1.0, Size = 2, NoZero), Arrows(6), above=true);
real f1(real x) { return (x - 2)*(x)*(x + 1)/6 + x + 2; }
draw(graph(f1, -3.25, 3.25), linewidth(1));
clip((xmin, ymin)--(xmin, ymax)--(xmax, ymax)--(xmax, ymin)--cycle);
label("$y=f(x)$", (3.5, 0.6), E);
[/asy]

If \( f(a) = b \) and \( f(b) = 3 \), then what is the value of \( a - b \)?

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