
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
Calculate the length of the arc of the curve given parametrically:

$$
\left\{\begin{array}{l}
x=\left(t^{2}-2\right) \sin t+2 t \cos t, \\
y=\left(2-t^{2}\right) \cos t+2 t \sin t,
\end{array} \quad 0 \leq t \leq \pi\right.
$$

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