
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
\[f(x) = \frac{x^2 - 2x + 8}{3x - 3}\]
and
\[g(x) = \frac{ax^2 + bx + c}{x - 1}.\]
You are given the following properties:

$\bullet$ The graphs of $f(x)$ and $g(x)$ have the same vertical asymptote.

$\bullet$ The oblique asymptotes of $f(x)$ and $g(x)$ are perpendicular, intersecting at $(0,3).$

$\bullet$ The graphs of $f(x)$ and $g(x)$ intersect at two points, one of which is on the line $x = -3.$

Find the point of intersection of the graphs of $f(x)$ and $g(x) that does not lie on the line $x = -3.$

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