
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
Meiyangyang is using two types of decorations to decorate a "Christmas tree". The decorations are hung on each vertex of small triangles. Meiyangyang can decorate in any order. If two vertices of a small triangle already have the same decoration, then the third vertex will have the other decoration; otherwise, the third vertex will have the same decoration. How many different designs of the "Christmas tree" are there? (No rotation or flipping is allowed)

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