
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
On a rotating round table, there are 8 white teacups and 7 black teacups. Fifteen dwarves wearing hats (8 white hats and 7 black hats) are sitting around the table. Each dwarf picks a teacup of the same color as their hat and places it in front of them. After this, the table is rotated randomly. What is the maximum number of teacups that can be guaranteed to match the color of the dwarf's hat after the table is rotated? (The dwarves are allowed to choose their seating, but they do not know how the table will be rotated.)

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