
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
A square piece of paper has side length $2$ and vertices $A, B, C, D$ in that order. When folded so that vertex $C$ meets edge $\overline{AD}$ at point $C'$, and edge $\overline{BC}$ intersects edge $\overline{AB}$ at point $E$, $C'D = 1$. Find the perimeter of triangle $\triangle AEC'$.
A) $1 + \sqrt{5}$  
B) $2 + \sqrt{3}$  
C) $\sqrt{7}$  
D) $\sqrt{13}$

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