
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 person has 4 colors of light bulbs (enough of each color), and needs to install one light bulb at each of the 6 points $A, B, C, A_{1}, B_{1}, C_{1}$ as shown in the diagram. It is required that the light bulbs at the two ends of the same segment are of different colors. What is the number of ways to install the light bulbs, ensuring that each color is used at least once? (Answer in digits).

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