
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 \( ABCD \) such that \( AB = BD \), \( \angle ABD = \angle DBC \), and \( \angle BCD = 90^\circ \). Point \( E \) is marked on segment \( BC \) such that \( AD = DE \). What is the length of segment \( BD \) if it is known that \( BE = 7 \) and \( EC = 5 \)?

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