
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

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

Given:
\[
\left\{\begin{array}{l}
x = \frac{t+1}{t} \\ 
y = \frac{t-1}{t}
\end{array}\right.
\]
where \( t_0 = -1 \)

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