
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) = e^x - a(x + 4), where the domain is (0, +∞) and a ∈ R.
1. Find the monotonic intervals of the function f(x).
2. If the inequality (x + 1)e^x + a(x^2 + 4x) ≥ 0 holds true for x ∈ (0, +∞), find the range of values for a.

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