
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 normal to the curve given parametrically by

\[ x = 2(t - \sin t), \quad y = 2(1 - \cos t) \]

1) at an arbitrary point; 2) at \( t = \frac{\pi}{2} \).

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