
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
Right triangle EFG with a right angle at F is constructed externally on the hypotenuse EG of isosceles right triangle DEF where DE = EF = 2. The sum of the perimeters of triangles DEF and EFG equals twice the perimeter of DEF. What is $\cos(2 \angle DFG)$?
A) 0  
B) 1/3  
C) 1/2  
D) 2/3  
E) 1

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