
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
To find the equations of the tangent and normal lines to the curve at the point corresponding to the parameter value \( t = t_{0} \).

Given:
\[
\begin{cases}
x = 2t - t^2 \\
y = 3t - t^3
\end{cases}
\]

where \( t_{0} = 1 \).

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