
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 values can the angle at the vertex of an isosceles triangle take if it is known that exactly three lines can be drawn to divide the area and perimeter of the triangle in half?


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