
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
Using 4 colors (red, pink, yellow, black) to color the 6 faces of a cube so that there is exactly one face colored yellow, one face colored black, two faces colored red, and two faces colored pink. Mr. Li is partially color-blind. For two colored cubes $W_{6}$ and $W_{6}^{\prime}$, if $W_{6}^{\prime}$ is obtained by switching the two red faces of $W_{6}$ to pink and the two pink faces to red, Mr. Li, due to his color-blindness, considers $W_{6}$ and $W_{6}^{\prime}$ to be identical. Determine the number of distinct colored cube patterns according to Mr. Li’s recognition method.

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