
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 $f(x) = \frac{e^{x}}{x^{2}-mx+1}$.

(I) Find the monotonic intervals of the function $y=f(x)$ when $m \in (-2, 2)$.

(II) If $m \in (0, \frac{1}{2}]$, determine the relationship between the minimum value $M$ of $f(x)$ and the maximum value $N$ of $g(x) = x$ when $x \in [1, m+1]$. Write out the judgment process.

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