
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 $$f(x)=\log_{0.5}(x^{2}-mx-m)$$.
(1) If the domain of function $f(x)$ is $\mathbb{R}$, find the range of the real number $m$;
(2) If the function $f(x)$ is increasing in the interval $$(-2, -\frac{1}{2})$$, find the range of the real number $m$.

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