
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
Each face and each vertex of a regular tetrahedron is colored red or blue. How many different ways of coloring are there? (Two tetrahedrons are said to have the same coloring if we can rotate them suitably so that corresponding faces and vertices are of the same color.)

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