
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 graph of $3x^2 + 2xy + 4y^2 - 15x - 24y + 54 = 0$ is an ellipse. Determine the sum of the maximum and minimum values of $\frac{y}{x}$ over all points $(x,y)$ on this ellipse.
A) 0.5
B) 1
C) 1.5
D) 2
E) 2.5

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