
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

The rules of the game are as follows: from 64 different items, on each turn, a player needs to form a set of items that has not been mentioned in the game before, in which the number of items equals the player's age in years. Players take turns making moves; any player can start the game. The player who cannot make a move loses. Sets of items are considered different if they differ by at least one item or if they contain a different number of items. The game involves Vasily and Fyodor; each player has the opportunity to make at least one move. It is known that: a) Vasily is 2 years older than Fyodor; b) Fyodor is at least 5 years old; c) Fyodor always wins. What is the minimum age of Vasily?

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