
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 $f(x) = \log_{2}\left(m+ \frac{m-1}{x-1}\right)$ ($m \in \mathbb{R}$, and $m > 0$).
1. Find the domain of the function $f(x)$.
2. If the function $f(x)$ is monotonically increasing on the interval $(4, +\infty)$, find the range of $m$.

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