
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
As $t$ takes on all real values, the set of points $(x,y)$ defined by
\[
x = t^2 - 4, \\
y = t^3 - 6t + 7
\]
forms a curve. Determine if this curve crosses itself, and if so, compute the ordered pair $(x, y)$ where this crossing occurs.

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