
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
\[
f(x) = \frac{x^2 - 4x + 3}{2x - 6}
\]
and
\[
g(x) = \frac{ax^2 + bx + c}{x - 3}.
\]
You are given the following properties:
- The graphs of \(f(x)\) and \(g(x)\) have the same vertical asymptote.
- The oblique asymptotes of \(f(x)\) and \(g(x)\) are perpendicular and intersect on the y-axis at \(y=1\).
- The graphs intersect at \(x = -1\) and one other point.

Find the coordinates of the other point of intersection of the graphs of \(f(x)\) and \(g(x)\).

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