
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

Write the equations of the tangent and normal lines to the curve at the point corresponding to the parameter value \( t = t_0 \).

\[
\left\{
\begin{array}{l}
x = t(1 - \sin t) \\
y = t \cdot \cos t
\end{array}
\right.
\]

where \( t_0 = 0 \).

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