
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 $f(x)=\lg (x^{2}-x-2)$ is set $A$, the range of the function $g(x)=x^{ \frac {1}{2}}$, $x\in[0,9]$ is set $B$,
$(1)$ Find $A\cap B$;
$(2)$ If $C=\{x|3x < 2m-1\}$, and $(A\cap B) \subseteq C$, find the range of values for the real number $m$.

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