
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
Find the largest x-coordinate at which the graph of the polynomial \( y = x^6 - 5x^5 + 5x^4 + 5x^3 + dx^2 \) intersects the parabola \( y = ex^2 + fx + g \) at exactly three points. Assume all intersections occur at x-values with multiplicity 2.
A) 0  
B) 1  
C) 2  
D) 3  
E) 4

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