
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 $a$.

[asy]
size(140);
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 -3x^2+6x+2;

}

draw(graph(f,-1,3),linewidth(1),Arrows(6));
[/asy]

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