
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 \( f(x)=\left\{\begin{array}{ll}(3-m)x-m, & x<1, \\ \log_{m}x, & x \geqslant 1\end{array}\right. \), for the function to be monotonically increasing on the set of real numbers \(\mathbf{R}\), what is the range of the real number \( m \)?

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