
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) = xe^x + 1/2 ax^2 + ax, where a ∈ R:
1. Discuss the monotonicity of the function f(x);
2. Find the range of the real number a when 2ef(x) + e + 2 ≥ 0 for x ∈ R.

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