
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
Points  $A$ ,  $B$ ,  $C$ , and  $D$  lie on a circle. Let  $AC$  and  $BD$  intersect at point  $E$  inside the circle. If  $[ABE]\cdot[CDE]=36$ , what is the value of  $[ADE]\cdot[BCE]$ ? (Given a triangle  $\triangle ABC$ ,  $[ABC]$  denotes its area.)

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