
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 domain of the function $f(x) = \lg(x^2-x-2)$ be the set $A$, and the domain of the function $g(x) = \sqrt{3-|x|}$ be the set $B$.  
(1) Find ① $A \cap B$; ② $(\complement_R A) \cup B$;  
(2) If $C = \{x | (x-m+1)(x-2m-1) < 0\}$, and $C \subseteq B$, find the range of the real number $m$.

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