
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
Six princesses have a magical chest. Once a minute, a dress can be taken out of it, which will be one of 10 colors and one of 9 styles. However, within one hour, it is impossible to take out two dresses from the chest that share both the same color and style. What is the minimum number of dresses the princesses need to take out from the chest to guarantee having 6 dresses of different colors but the same style?

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