
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 $f(x) = \frac{(3-x)e^x + a}{x} (x > 0, a \in \mathbb{R})$.

(1) Determine the monotonicity of the function $f(x)$ when $a > -\frac{3}{4}$.

(2) When the function $f(x)$ has two extreme points,

$\quad$(a) Find the range of values for $a$.

$\quad$(b) If the maximum value of $f(x)$ is less than the integer $m$, find the minimum value of $m$.

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