
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 $g(x)=Ax^2+Bx+C$ is shown below. The distance between grid lines on the graph is $1$ unit.

Consider the quadratic function $g(x) = 2x^2 + Bx + C$. The graph of $y=g(x)$ passes through the points $(1,3)$ and $(2,0)$. What is the value of $A+B+C+2C$?

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