
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 psychic is faced with a deck of 36 cards placed face down (four suits, with nine cards of each suit). He names the suit of the top card, after which the card is revealed and shown to him. Then the psychic names the suit of the next card, and so on. The goal is for the psychic to guess as many suits correctly as possible.

The backs of the cards are asymmetric, and the psychic can see the orientation in which the top card is placed. The psychic's assistant knows the order of the cards in the deck but cannot change it. However, the assistant can place the backs of each card in one of two orientations.

Could the psychic have agreed with the assistant before the assistant knew the order of the cards to ensure guessing the suit of at least a) 19 cards; b) 23 cards?

If you have devised a method to guess a number of cards greater than 19, please describe it.

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