
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 coordinates of the center of curvature and plot the curve and the circle of curvature for the curve:
1) \( y = 4x - x^2 \) at its vertex;
2) \( x = t - \sin t, \, y = 1 - \cos t \) at the point where \( t = \frac{\pi}{2} \).

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