
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
$$f(x) = \log_{\frac{1}{2}} \left(x^2 - mx - m\right)$$

(1) If $m=1$, find the domain of the function $f(x)$.
(2) If the range of the function $f(x)$ is $\mathbb{R}$, find the range of values for the real number $m$.
(3) If the function $f(x)$ is increasing on the interval, find the range of values for the real number $m$.

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