
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
Let $\triangle ABC$ have $AC = 2$ and $AB = BC$. It has $\measuredangle BAC = 70^{\circ}$, and $\measuredangle ABC = \measuredangle ACB$. Let $D$ be on side $AC$ such that $AD = DC = 1$, and $E$ is the midpoint of $BC$. If $\measuredangle DEC = 60^{\circ}$, find the area of $\triangle ABC$ plus the area of $\triangle CDE$.

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