
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 > 0\\) and \\(a \neq 1\\), the function \\(f(x) = \log_a(x+1)\\), \\(g(x) = \log_a \frac{1}{1-x}\\), let \\(F(x) = 2f(x) + g(x)\\).

\\((1)\\) Find the domain \\(D\\) of the function \\(F(x)\\) and its zeros;

\\((2)\\) If the equation \\(F(x) - m = 0\\) has only one solution in the interval \\([0,1)\\), find the range of the real number \\(m\\).

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