
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
Given the cubic equation \( y = ax^3 + bx^2 + cx + d \) drawn on a set of axes, and another graph of the equation formed by replacing \( x \) with \( -x \), determine the points of intersection if \( a \neq 0, b \neq 0, c \neq 0 \), and \( d \neq 0 \).
A) Only at $(0, d)$
B) In two distinct real points
C) In three distinct real points
D) Only in complex plane, no real intersection
E) In one point on each axis

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