
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
Determine the intersection points of the curves \(y = x^3 - 2x^2 - x + 2\) and \(2x + 3y = 3\). Let the x-coordinates of the intersection points be \(x_1, x_2,\) and \(x_3\), and the y-coordinates be \(y_1, y_2,\) and \(y_3\). Compute the sums \(x_1 + x_2 + x_3\) and \(y_1 + y_2 + y_3\), and provide the ordered pair \((A, B)\).

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