
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 and the normal to the curve at the point corresponding to the parameter value \( t = t_{0} \):

$$
\begin{aligned}
& \left\{\begin{array}{l}
x=\frac{1+t}{t^{2}} \\
y=\frac{3}{2 t^{2}}+\frac{2}{t}
\end{array}\right. \\
& t_{0}=2
\end{aligned}
$$

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