
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 universal set U = R, set A = {x | (x - 2)(x - 9) < 0}, and set B = {x | -2 - x ≤ 0 ≤ 5 - x}.

1. Find A ∩ B and B ∪ (∁<sub>U</sub>A).
2. Given set C = {x | a ≤ x ≤ 2 - a}, if C ∪ (∁<sub>U</sub>B) = R, find the range of values for the real number a.

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