
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 $g(x) = dx^3 + ex^2 + fx + g$, where $d$, $e$, $f$, and $g$ are integers. Suppose that $g(1) = 0$, $70 < g(5) < 80$, $120 < g(6) < 130$, $10000m < g(50) < 10000(m+1)$ for some integer $m$. What is $m$?

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