
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
Polina has a deck of 36 cards (4 suits, 9 cards each). She selects half of the cards as she wishes and gives them to Vasilisa, keeping the other half for herself. Then, each turn, the players take turns revealing one card of their choice (the opponent sees the suit and rank of the revealed card), starting with Polina. If in response to Polina's move, Vasilisa can place a card of the same suit or rank, Vasilisa earns one point. What is the maximum number of points Vasilisa can be guaranteed to earn?

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