
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
Given an isosceles triangle \( \triangle ABC \) with base angles \( \angle ABC = \angle ACB = 50^\circ \), points \( D \) and \( E \) lie on \( BC \) and \( AC \) respectively. Lines \( AD \) and \( BE \) intersect at point \( P \). Given \( \angle ABE = 30^\circ \) and \( \angle BAD = 50^\circ \), find \( \angle BED \).

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