
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 a square piece of paper with a side length $2$ and vertices $A,B,C,$ and $D$ in that order, the paper is folded such that vertex $C$ meets edge $\overline{AB}$ at point $C'$, making $C'B = \frac{2}{3}$. If edge $\overline{BC}$ intersects edge $\overline{AD}$ at point $E$, calculate the perimeter of triangle $\bigtriangleup AEC'$.

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