
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. Given that $g(2) = 0$, $70 < g(6) < 80$, $110 < g(7) < 120$, $2000m < g(50) < 2000(m+1)$ for some integer $m$. Determine the value of $m$.

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