
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
We need to color the three-element subsets of a seven-element set in such a way that if the intersection of two subsets is empty, then their colors are different. What is the minimum number of colors needed for this?

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