
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
Is it possible to construct a closed broken line such that each of its segments intersects with some other segment (at an internal point) and the intersecting segments are mutually perpendicular? Can such a line have 315 segments? Can it be symmetric with respect to some axis?

Given a scalene triangle \(ABC\), divide it with a line passing through point \(A\) into two triangles, such that the ratio of their perimeters is equal to the ratio of their areas.

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