
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
The graph of $y = ax^2 - bx + c$ is given below, where $a$, $b$, and $c$ are integers. Find $a+b+c$.

[asy]
size(150);

Label f;

f.p=fontsize(4);

xaxis(-3,3,Ticks(f, 1.0));

yaxis(-4,4,Ticks(f, 1.0));

real f(real x)

{

return x^2-x-1;

}

draw(graph(f,-2.0,2.5),linewidth(1), Arrows(6));
[/asy]

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