
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 the set $A = (2, 3]$, $B = (1, 3)$, and $C = [m, +\infty)$, where the universal set is the real numbers $\mathbb{R}$.
(1) Find the intersection of the complement of $A$ with respect to $\mathbb{R}$ with set $B$.
(2) If the intersection of the union of $A$ and $B$ with set $C$ is non-empty, determine the range of values for the real number $m$.

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