
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 \( t = t_0 \).

\[
\left\{
\begin{array}{l}
x = \arcsin \frac{t}{\sqrt{1 + t^2}} \\
y = \arccos \frac{1}{\sqrt{1 + t^2}}
\end{array}
\right.
\]

\( t_0 = 1 \)

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