
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
\[ f(x) = \frac{x^2 - 8x + 8}{2x - 6} \]
and
\[ g(x) = \frac{ax^2 + bx + c}{x - e}. \]
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 they intersect on the $y$-axis.
- The graphs of $f(x)$ and $g(x)$ have two intersection 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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