
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
A unit square is called "colorful" if three of its four sides are colored in three different colors. Consider the $1 \times 3$ grid, which contains 10 unit length line segments. These 10 line segments are to be colored using red, yellow, or blue, such that all three unit squares are colorful. How many ways can this coloring be done? (Express the answer as a numerical value.)

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