
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 $ABC$, $BC = 1$ unit and $\measuredangle BAC = 40^\circ$, $\measuredangle ABC = 90^\circ$, hence $\measuredangle ACB = 50^\circ$. Point $D$ is midway on side $AB$, and point $E$ is the midpoint of side $AC$. If $\measuredangle CDE = 50^\circ$, compute the area of triangle $ABC$ plus twice the area of triangle $CED$.
A) $\frac{1}{16}$
B) $\frac{3}{16}$
C) $\frac{4}{16}$
D) $\frac{5}{16}$
E) $\frac{7}{16}$

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