
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
Isosceles triangle  $\triangle{ABC}$  has  $\angle{BAC}=\angle{ABC}=30^\circ$  and  $AC=BC=2$ . If the midpoints of  $BC$  and  $AC$  are  $M$  and  $N$ , respectively, and the circumcircle of  $\triangle{CMN}$  meets  $AB$  at  $D$  and  $E$  with  $D$  closer to  $A$  than  $E$  is, what is the area of  $MNDE$ ?

*2019 CCA Math Bonanza Individual Round #9*

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