
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
A function is given by the following expression, where $x$ is the variable, and $a$ and $b$ are constants, neither of which equals 1. What could be the domain of the function? What is the range?

$$
\frac{x}{1-x}+\frac{a}{(1-x) \cdot(1-a)}+\frac{b-x}{(1-x) \cdot(1-a) \cdot(1-b)}
$$

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