
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  $ABCD$  be a convex quadrilateral such that  $AB + BC = 2021$  and  $AD = CD$ . We are also given that  $\angle ABC = \angle  CDA = 90^o$ . Determine the length of the diagonal  $BD$ .

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