
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
Let \(ABCD\) be a quadrilateral such that \(\widehat{DAB} = 60^\circ\), \(\widehat{ABC} = 90^\circ\), and \(\widehat{BCD} = 120^\circ\). Let \(M\) be the intersection point of the diagonals \([AC]\) and \([BD]\). Given that \(BM = 1\) and \(DM = 2\), calculate the area of quadrilateral \(ABCD\).

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