
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 - a(x^2 + 2x), where a > 0,
(I) Find the monotonic intervals of f(x) when a = 1.
(II) Find the range of real number a that makes f(x) ≤ 0 always hold true when x < 0.

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