
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 functions $f(x)=\log_{2}(1-x)$ and $g(x)=\log_{2}(1+x)$, let $h(x)=f(x)-g(x)$.
(1) Find the domain of the function $h(x)$, determine its even or odd property, and provide the proof process.
(2) Determine the monotonicity of the function $h(x)$ in its domain, and provide the necessary reasoning process.

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