
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^(ax)ln(x+2), where e is the base of the natural logarithm.
(1) If a belongs to the set of real numbers, discuss the monotonicity of the function F(x) = e^(-ax)f'(x).
(2) If a < 1/2, the function g(x) = f(x) - x - 1 has a zero point in the interval (-1, +∞). Find the range of values for the real number a.

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