
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 the diagram, three circles of radius 2 with centers $X$, $Y$, and $Z$ are tangent to each other and to side $DE$ of $\triangle DEF$, which is equilateral. The circles are aligned in such a way that each circle touches exactly two others and the side DE.

Find the perimeter of triangle $DEF$.

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