
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 that the domain of the function $f(x)=\sqrt{\log_{\frac{1}{2}}(x-1)}$ is set $A$ and the range of the function $g(x)=3^{m-2x-x^2}-1$ is set $B$, and $A \cup B = B$, find the range of real number values for $m$.

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