
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
Equilateral triangle \(ABC\) has circumcircle \(\Omega\). Points \(D\) and \(E\) are chosen on minor arcs \(AB\) and \(AC\) of \(\Omega\) respectively such that \(BC=DE\). Given that triangle \(ABE\) has area 3 and triangle \(ACD\) has area 4, find the area of triangle \(ABC\).

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