
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
Given $\triangle ABC$ where $E$ is the midpoint of side $BC$ and $D$ is placed on side $AC$ such that $\overline{AD} = \frac{1}{2}\overline{AC}$, with $AC = 1$, $\measuredangle BAC = 30^\circ$, $\measuredangle ABC = 80^\circ$, and $\measuredangle ACB = 70^\circ$, and $\measuredangle DEC = 40^\circ$, find the sum of the area of $\triangle ABC$ and twice the area of $\triangle CDE$.

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