
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
Let $g(x)=Ax^2+Bx+C$, where $A$, $B$, and $C$ are integers. Suppose that $g(2)=0$, $100<g(9)<110$, $150<g(10)<160$, $10000m<g(200)<10000(m+1)$ for some integer $m$. What is $m$?

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