
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 where the graphs of $y = x^4 - 4x^3 + 4x + 1$ and $2x - 3y = 6$ intersect. If the $x$-coordinates of the intersection points are $x_1, x_2, x_3, x_4,$ and the sum of these coordinates is $S$, and the sum of their respective $y$-coordinates $y_1, y_2, y_3, y_4$ is $T$, compute the ordered pair $(S, T)$.

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