
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 P = {x | -2 ≤ x ≤ 10} and Q = {x | 1 - m ≤ x ≤ 1 + m}.

(1) Determine the complement of P in the real numbers, denoted ∁<sub>R</sub>P.
(2) If P is a subset of Q, find the range of the real number m.
(3) If the intersection of P and Q equals Q, find the range of the real number m.

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