
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
Let $t$ represent all real values. Consider the curve formed by the set of points $(x, y)$ defined by the equations:
\[
x = t^3 - 3t + 1, 
\]
\[
y = t^4 - 4t^2 + 4.
\]
Determine the ordered pair $(x,y)$ where the curve crosses itself.

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