
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 graphs of $y = x^3 - 3x + 2$ and $y = x^2 - 2x + 2$ intersect at points $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$. Compute the sums $x_1 + x_2 + x_3 = A$ and $y_1 + y_2 + y_3 = B$. Determine the ordered pair $(A,B)$.

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