
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 $y = x^3 - 4x + 3$ and $x^2 + 4y = 8$ intersect in the points $(x_1,y_1),$ $(x_2,y_2),$ and possibly more. If the sum of all $x$-coordinates of the intersection points is $A$ and the sum of all $y$-coordinates of the intersection points is $B$, compute the ordered pair $(A,B)$.

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