
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
What fraction of the area of triangle $ABC$ is occupied by those points $K$ which lie inside the triangle and for which the point-similarity with center $K$ and ratio $-1/2$ maps $A$ and $B$ to internal points of the triangle, but maps $C$ to an external point?

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