
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
Of the four sides of a unit square, if two sides are colored with color \( i \) and the other two sides are colored with two different colors other than \( i \), then the unit square is called "dominated by color \( i \)". As shown in the diagram, a $1 \times 3$ grid contains 10 unit-length line segments. We want to color these 10 line segments with three colors: red, yellow, and blue, such that there is one unit square dominated by red, one dominated by yellow, and one dominated by blue. The number of such coloring ways is ___ .

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