
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 7 cells in a $4 \times 4$ grid using the same color. If a column has colored cells, they must be colored from the bottom up consecutively. Additionally, 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 different coloring patterns are possible?

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