
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
A portion of the graph of \( f(x) = ax^2 + bx + c \) is shown below. The distance between grid lines on the graph is 1 unit.

What is the value of \( a+b+2c \)?

[asy]
size(150);
rr_cartesian_axes(-4,3,-2,9);
real f(real x) {return -2*(x-2)^2 + 8;}
draw(graph(f,-1,5,operator ..), red);
[/asy]

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