
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) = (ax^2 + x + a)e^-x (a ∈ R).
(I) If a ≥ 0, find the monotonic intervals of the function f(x);
(II) If for any a ≤ 0, f(x) ≤ b ln(x + 1) holds true for x ∈ [0, +∞), find the range of the real number b.

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