
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
One hundred bear cubs found berries in the forest: the youngest managed to grab 1 berry, the next bear cub grabbed 2 berries, the next 4 berries, and so on, with the oldest getting $2^{99}$ berries. A fox proposed to "fairly" distribute the berries among the bear cubs. She approached two bear cubs and redistributed their berries equally between them, and if an extra berry remains, she ate it herself. She continued these actions until all the bear cubs had an equal number of berries. What is the maximum number of berries the fox can eat?

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