
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
Parallelogram  $ABCD$  has  $AB=CD=6$  and  $BC=AD=10$ , where  $\angle ABC$  is obtuse. The circumcircle of  $\triangle ABD$  intersects  $BC$  at  $E$  such that  $CE=4$ . Compute  $BD$ .

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