
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]


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Given that \\(a\\) is a constant, and the function \\(f(x) = x^{2} + ax - \ln x\\), \\(g(x) = e^{x}\\) (where \\(e\\) is the base of the natural logarithm).
\\((1)\\) Draw a tangent line from the origin \\(O\\) to the curve \\(y = f(x)\\), and let the tangent point be \\(P(x_{0}, y_{0})\\). Find the value of \\(x_{0}\\).
\\((2)\\) Let \\(F(x) = \frac{f(x)}{g(x)}\\). If the function \\(F(x)\\) is monotonic on the interval \\((0,1]\\), find the range of values for \\(a\\).

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