
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
Color 6 cells in a $4 \times 4$ grid with one color. If a column has colored cells, they must be colored consecutively starting from the bottom of the column. In any two adjacent columns, the number of colored cells in the left column must be greater than or equal to the number of colored cells in the right column. How many such coloring patterns are there?

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