
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 each of the 2013 cards, there is a number, and all these 2013 numbers are unique. The cards are turned face down. In one move, you are allowed to point to ten cards, and in response, you will be informed of one of the numbers written on them (it is unknown which one).

For what largest $t$ is it guaranteed to be possible to find $t$ cards for which the number written on each is known?

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