
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 picture below, there are four triangles labeled \( S, T, U \), and \( V \). Two of the triangles will be colored red and the other two triangles will be colored blue. How many ways can the triangles be colored such that the two blue triangles have a common side?

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