
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
On a table, there are 55 piles of candies. In one pile, there is 1 candy, in another 2 candies, in the third 3 candies, ..., and in the last pile 55 candies. Petya and Vasya play the following game, taking turns; Petya starts. In one move, a player takes one candy from any pile. If the player took the last candy from a pile, he eats it; otherwise, he throws it away. The game continues until all candies are eaten or thrown away. What is the maximum number of candies Petya can guarantee to eat?

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