
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

A tea set consists of six identical cups and six identical saucers. Six different sets were packed into two boxes: one box contains all the saucers, and the other box contains all the cups. All the items are wrapped in opaque paper and cannot be distinguished by touch. Find the minimum number of items that must be taken out of these boxes to guarantee getting at least one pair consisting of a cup and saucer from the same set. Justify your answer. (You know which box contains the cups and which box contains the saucers.)

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