
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 the function $f(x) = \log_a(1 - a^x)$ where $a > 0$ and $a \neq 1$,
1. Find the domain of function $f(x)$.
2. Find the range of real numbers $x$ that satisfy the inequality $\log_a(1 - a^x) > f(1)$.

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