
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 two sets $A=\{x \mid 1 \leq 2^x \leq 4\}$ and $B=\{x \mid x-a > 0\}$:
1. If $a=1$, find the intersection $A \cap B$.
2. If the union $A \cup B$ equals $B$, find the range of $a$.

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