
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
Pyotr has a deck of 36 cards (4 suits with 9 cards in each). He chooses half of the cards (whichever he wants) and gives them to Vasya, keeping the other half for himself. In each subsequent turn, players alternately place one card face-up on the table, starting with Pyotr. If Vasya can respond to Pyotr's card by placing a card of the same suit or rank, Vasya earns 1 point. What is the maximum number of points Vasya can be guaranteed to earn?

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