
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 \( P(x) = x^7 - x^6 - 21x^5 + 35x^4 + 84x^3 - 49x^2 - 70x + d \). The graph of \( P(x) \) intersects the line \( y = 2x - 3 \) at exactly three different points. Calculate the largest \( x \) value where the intersection occurs.
A) 1
B) 2
C) 3
D) -2
E) -1

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