
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
Xiaohu uses 6 equilateral triangles with side lengths of 1 to form shapes on a table without overlapping. Each triangle must share at least one side fully with another triangle. As shown in the image, there are two possible shapes formed. Among all the possible shapes, what is the smallest perimeter?

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