
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, each with 9 cards). She selects half of the cards, as she wishes, and gives them to Vasilisa, while keeping the other half for herself. Then, each player takes turns opening 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 turn, Vasilisa can play a card of the same suit or rank, she earns one point. What is the maximum number of points Vasilisa can guarantee to earn?

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