
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 $f(x)=\log_{2}(1-x)-\log_{2}(1+x)$.
(1) Find the domain of the function $f(x)$;
(2) Determine the parity (odd or even) of $f(x)$;
(3) Does the equation $f(x)=x+1$ have any roots? If it does have a root $x_{0}$, find an interval $(a,b)$ with a length of $\frac{1}{4}$ such that $x_{0}\in(a,b)$; otherwise, explain the reason. (Note: The length of the interval $(a,b)$ is $b-a$.)

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