
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
At a round rotating table with 8 white and 7 black cups, 15 gnomes are seated. They wear 8 white and 7 black caps. Each gnome picks a cup whose color matches the color of their cap and places it in front of them. After that, the table is randomly rotated. What is the maximum number of matches?

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