
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
Consider the polynomial $y = x^6 - 13x^5 + 42x^4 - 30x^3 + ax^2$ and a line $y = 3x + c$. The graph of the polynomial lies below the line, except at three values of $x$, where the graph and the line intersect. Determine the largest of these intersection points.
A) 3
B) 4
C) 5
D) 6
E) 7

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