
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
Given the function $f(x) = x^2 + mx + 4$.  
(I) When $x \in (1, 2)$, the inequality $f(x) < 0$ always holds. Find the range of real numbers $m$.  
(II) If the solution set of the inequality $\left| \frac{f(x) - x^2}{m} \right| < 1$ contains and only contains the integers 1 and 2, find the range of real numbers $m$.

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