
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
Consider the parametric equations as $t$ varies over all real numbers:
\begin{align*}
x &= t^2 + 3, \\
y &= t^3 - 6t + 4.
\end{align*}
Determine the coordinates of the point(s) where this curve intersects itself.

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