
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 $f(x) = 2\ln x + x^2 - ax + 2$ ($a \in \mathbb{R}$),
(I) Discuss the monotonicity of the function $f(x)$;
(II) If there exists $x_0 \in (0, 1]$ such that for any $a \in [-2, 0)$, the inequality $f(x_0) > a^2 + 3a + 2 - 2me^{a(a+1)}$ (where $e$ is the base of the natural logarithm) holds, find the range of the real number $m$.

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