
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

Let's solve the following system of equations:

\[
\begin{gathered}
\frac{x}{x-a}+\frac{y}{y-b}=2 \\
a x+b y=2 a b 
\end{gathered}
\]

What cases arise if \(a = \pm b\)?

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