
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
\[ f(x) = \frac{x^2 - 8x + 15}{3x - 6} \]
and
\[ g(x) = \frac{bx^2 + 4bx - c}{x - 2} \] 
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 three intersection points, one of which is on the line \( x = -3 \).

Find the points of intersection of the graphs of \( f(x) \) and \( g(x) \) that do not lie on the line \( x = -3 \).

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