
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
The lines with the two equations below intersect at the point $(2,-3)$.

\[
\begin{array}{r}
\left(a^{2}+1\right) x-2 b y=4 \\
(1-a) x+b y=9
\end{array}
\]

What are the possible ordered pairs $(a, b)$?

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