
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
There is a magician and an assistant with a deck of cards where one side ("back") of all the cards is the same, and the other side is painted in one of 2017 colors (with 1,000,000 cards of each color in the deck). The magician and the assistant are going to perform the following trick. The magician leaves the room, and the audience sets down $n>1$ cards face down in a row on the table. The assistant looks at these cards and then flips all but one of them over, without changing their order. Then the magician comes back in, looks at the table, points to one of the face-down cards, and correctly names its color. What is the smallest value of $n$ for which the magician and the assistant can prearrange a strategy to guarantee that the trick is always successful?

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