
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
In the coordinate plane, given a circle  $K: x^2+y^2=1,\ C: y=x^2-2$ . Let  $l$  be the tangent line of  $K$  at  $P(\cos \theta,\ \sin \theta)\ (\pi<\theta <2\pi).$  Find the minimum area of the part enclosed by  $l$  and  $C$ .

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