
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 $A=\{y \mid y=\log_{2} x, x \geq 4\}$ and $B=\{y \mid y = \left(\frac{1}{2}\right)^x, -1 \leq x \leq 0\}$.
1. Find the intersection $A \cap B$;
2. Let set $C = \{x \mid a \leq x \leq 2a-1\}$, and assume $C \cup B = B$. Find the range of real number $a$.

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