
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
Formulate the equations of the tangent and the normal to the curve at the point corresponding to the parameter value $t=t_{0}$.

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

$t_{0}=2$


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