
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 parametric equation for the curve is
$$
\begin{cases}
x = 1 - \frac{1}{t},\\
y = 1 - t^2
\end{cases}
(t \text{ as the parameter, } t \neq 0),
$$
determine its Cartesian equation.

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