
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
Petya has a deck of 36 cards (4 suits with 9 cards each). He chooses half of the cards (whichever he wants) and gives them to Vasya, keeping the other half for himself. Then, each player takes turns placing one card on the table (of their choice, face-up); Petya starts. If in response to Petya's move, Vasya is able to place a card of the same suit or rank, Vasya earns 1 point. What is the maximum number of points that Vasya can guarantee?

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