
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
Multiply and simplify the following expression:

\[
\frac{1-a x}{1+a x} \cdot \sqrt{\frac{1+b x}{1-b x}}
\]

with the condition:

\[
x=\frac{1}{a} \cdot \sqrt{\frac{2 a-b}{b}}
\]

and the constraints:

\[
0 < \frac{b}{2} < a < b.
\]

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