
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 a quadrilateral \( A B C D \) with the properties: \( A B = B D \), \( \angle A B D = \angle D B C \), \( \angle B C D = 90^\circ \). Point \( E \) is marked on segment \( B C \) such that \( A D = D E \). What is the length of segment \( B D \), given that \( B E = 7 \) and \( E C = 5 \)?

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