
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 \\(a \in \mathbb{R}\\), the function \\(f(x) = e^{x} - ax\\).
\\((1)\\) If the function \\(f(x)\\) is decreasing on the interval \\((-e, -1)\\), find the range of values for the real number \\(a\\).
\\((2)\\) If the function \\(F(x) = f(x) - (e^{x} - 2ax + 2\ln x + a)\\) has no zeros in the interval \\(\left(0, \frac{1}{2}\right)\\), find the maximum value of the real number \\(a\\).

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