
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 a quadratic function, $y = p(x) = ax^2 + bx + c$:

[asy]
import graph; size(8cm);
real lsf=0.5; pen dps=linewidth(0.7) + fontsize(10); defaultpen(dps); pen ds=black; real xmin=-2.99, xmax=15.5, ymin=-10.5, ymax=10.5;
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 8 - (x - 9)*(x - 10)/7; }
draw(graph(f1, -2.99, 15.5), linewidth(1));
clip((xmin, ymin) -- (xmin, ymax) -- (xmax, ymax) -- (xmax, ymin) -- cycle);
label("$y = p(x)$", (16, 3.5), E);
[/asy]

The axis of symmetry for the graph given appears to be between x=9 and x=10. The point $(0, -8)$ lies on the graph. Evaluate $p(20)$.

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