
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
János and Gábor play the following game: János draws a card from a 32-card Hungarian deck. Gábor must guess the suit of the drawn card. If he guesses correctly, he wins 2 Ft from János; if not, he gives János 1 Ft. Before making his guess, Gábor can name four cards, and János must tell him if the drawn card is among those four. How should Gábor choose the four cards to maximize his expected winnings?

Is the game fair? (We consider the game fair if the expected winnings for both players are $0 \mathrm{Ft}$.)

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