
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 magician and his assistant have a stack of cards, all with the same back and one of 2017 possible colors on the front (with one million cards for each color). The trick is as follows: the magician leaves the room, and the audience picks $n$ cards and places them face up in a row on the table. The assistant then turns over $n-1$ of these cards, leaving only one card face up. The magician re-enters the room, observes the cards on the table, and must guess the color of the face-down card. Find the minimum value of $n$ such that the magician and the assistant can perform this trick using a predetermined strategy.

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