
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 edge of a tetrahedron is colored either blue or red, and every face of the tetrahedron has at least one blue edge. Determine the smallest number of blue edges possible.

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