
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
Let sets $A=(2,3]$, $B=(1,3)$, and $C=[m,+\infty)$, with the universal set being $\mathbb{R}$.

$(1)$ Find $(C_{\mathbb{R}}A) \cap B$;

$(2)$ If $(A \cup B) \cap C \neq \varnothing$, find the range of the real number $m$.

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