
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 $f(x) = ax^2 + bx + c$, where $a, b, c$ are integers. It's given that $f(2) = 0$, $200 < f(10) < 300$, $400 < f(9) < 500$, and for an integer $j$, $1000j < f(100) < 1000(j + 1)$. What is $j$?

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