
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 function f(x) = $\sqrt{-x^2 + 5x - 6}$ with domain A, set B = {x | 2 ≤ 2^x^ ≤ 16}, set C = [m+1, 3m], and the universal set is the set of real numbers R.

1. Find the intersection A ∩ B and the complement of B in R (∁<sub>R</sub>B).
2. If A ∪ C = A, find the set of possible values for the real number m.

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