
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 $t=t_{0}$.

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

$t_{0}=1$

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