
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 that the function $f(x) = \lg(x - a)$ has a domain A, and the set B is defined as $\{y | y = 2^x - 1, x \in \mathbb{R}\}$.
1. If $A = B$, find the value of the real number $a$.
2. If $(\complement_{\mathbb{R}} A) \cap B \neq \emptyset$, find the range of the real number $a$.

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