
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
Let  $ABC$  be a triangle in which  $\measuredangle{A}=135^{\circ}$ . The perpendicular to the line  $AB$  erected at  $A$  intersects the side  $BC$  at  $D$ , and the angle bisector of  $\angle B$  intersects the side  $AC$  at  $E$ .
Find the measure of  $\measuredangle{BED}$ .

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