
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
Let the function $f(x) = (x+2)e^x$.  
(1) Find the intervals of monotonicity for $f(x)$.  
(2) When $x \geq 0$, it always holds that $\frac{f(x) - e^x}{ax + 1} \geq 1$, find the range of the real number $a$.

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