
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 $\triangle ABC$, $E$ is the midpoint of side $BC$ and $D$ is on side $AC$ such that $AD = DC = \frac{1}{2}AC$. 
If the length of $AC$ is $2$ and $\measuredangle BAC = 30^\circ, \measuredangle ABC = 80^\circ, \measuredangle ACB = 70^\circ$ and 
$\measuredangle DEC = 70^\circ$, then the area of $\triangle ABC$ plus twice the area of $\triangle ADE$ equals?
A) $2\sin 80^\circ$
B) $2\sin 70^\circ$
C) $2\sin 80^\circ + \sin 70^\circ$
D) $2\sin 70^\circ + \sin 80^\circ$

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