
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 $\triangle ABC$, point $D$ is the midpoint of side $BC$ and point $E$ is on side $AB$. The lengths of $AB = 1$ and $\measuredangle BAC = 70^\circ, \measuredangle ABC = 50^\circ, \measuredangle ACB = 60^\circ$ and $\measuredangle EDC = 80^\circ$. Find the area of $\triangle ABC$ plus twice the area of $\triangle CDE$.
A) $\frac{\sin 35^\circ}{2}$
B) $\frac{\sin 50^\circ}{2}$
C) $\frac{\sin 70^\circ + \sin 80^\circ}{2}$
D) $\frac{\sin 80^\circ}{2}$

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