
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
Two people are dividing a piece of cheese. First, the first person cuts the cheese into two pieces, then the second person cuts any piece into two, and so on, until there are five pieces. Then the first person takes one piece, then the second person takes one of the remaining pieces, and they continue taking turns until all the pieces are taken. Determine the maximum amount of cheese each player can guarantee for themselves.

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