
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 sets $A = \{x \mid y = \sqrt{x^2-5x-14}\}$, $B = \{x \mid y = \lg(-x^2-7x-12)\}$, and $C = \{x \mid m+1 \leq x \leq 2m-1\}$:
1. Find the complement of $A \cup B$ with respect to $\mathbb{R}$;
2. If $A \cup C = A$, determine the range of the real number $m$.

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