
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
Solve the following equation:

$$
\frac{1-a x}{1+a x} \sqrt{\frac{1+b x}{1-b x}}=1 .
$$

For which values of $a$ and $b$ will the roots of the equation be real?

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