
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 $t = t_{0}$.

Given:

$$ \left\{\begin{array}{l}x=2 \ln (\operatorname{ctg} t)+\operatorname{ctg} t \\ y=\operatorname{tg} t+\operatorname{ctg} t\end{array}\right. $$

where \( t_{0} = \frac{\pi}{4} \).

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