
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
In quadrilateral  $ABCD$ , diagonals  $AC$  and  $BD$  intersect at  $O$ . If the area of triangle  $DOC$  is  $4$  and the area of triangle  $AOB$  is  $36$ , compute the minimum possible value of the area of  $ABCD$ .

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