
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 straight line \( e \) passes through the inflection point of the cubic parabola \( y = -\frac{1}{3} x^{3} + 3x \) and intersects the curve at two other points. The straight line, the ordinates of the intersection points, and the \( X \)-axis determine two right-angled triangles. Examine the change of the sum of the areas of these two triangles if they are located in the plane region enclosed by the curve and the \( X \)-axis, and \( e \) rotates counterclockwise?

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