
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 universal set \( U = \mathbb{R} \), and the sets \( A = \{x | -1 \leq x < 3\} \) and \( B = \{x | 2x - 4 \geq x - 2\} \).
1. Find the complement of the intersection of sets \( A \) and \( B \), \( \complement_{U}(A \cap B) \).
2. If the set \( C = \{x | 2x + a > 0\} \) satisfies \( B \cup C = C \), find the range of the real number \( a \).

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