
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 $f(x) = \frac{x^2 + ax + 1}{x}, (x > 0, a \in \mathbb{R})$

(I) Discuss the number of zeros of the function $f(x)$ when $a \leqslant -2$;

(II) If the function $g(x) = e^x - \ln{x} + 2x^2 + 1$, and for any $x \in (0, +\infty)$, there is always $xf(x) \leqslant g(x)$, find the maximum value of the real number $a$.

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