
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
Consider the sets $A = \{x \mid -1 \leq x < 3\}$, $B = \{x \mid 2x - 4 \geq x - 2\}$, and $C = \{x \mid x \geq a - 1\}$.
1. Find $A \cap B$.
2. If $B \cup C = C$, determine the range of the real number $a$.

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