
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 an obtuse isosceles triangle, the product of the lengths of the two congruent sides is twice the product of the base length and the triangle's height to the base. What is the measure, in degrees, of the vertex angle of this triangle?

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