
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 sets $A=\{ x | 3 < x < 10 \}$, $B=\{ x | x^2-9x+14 < 0 \}$, $C=\{ 5-m < x < 2m \}$,

$(1)$ Find $A \cap B$, $(C_{R}A) \cup B$

$(2)$ If $x \in C$ is a sufficient but not necessary condition for $x \in (A \cap B)$, find the range of the real number $m$.

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