
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 regular hexagon  $ABCDEF$ , let point  $P$  be the intersection of lines  $BC$  and  $DE$ , and let point  $Q$  be the intersection of lines  $AP$  and  $CD$ . If the area of  $\triangle QEP$  is equal to  $72$ , find the area of regular hexagon  $ABCDEF$ .

*Proposed by **DeToasty3***

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