
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 and discuss the solution:

$$
\frac{a x+b}{a+b x}+\frac{c x+d}{c+d x}=\frac{a x-b}{a-b x}+\frac{c x-d}{c-d x}
$$

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