
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 is playing a computer game called "Pile of Stones." Initially, there are 16 stones in the pile. Players take turns to take 1, 2, 3, or 4 stones from the pile. The player who takes the last stone wins. Petya is playing for the first time and therefore takes a random number of stones each time, while still following the rules of the game. The computer plays according to the following algorithm: on each turn, it takes as many stones as necessary to put itself in the most advantageous position. Petya always starts the game. What is the probability that Petya will win?

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