
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 older cub - 2 berries, the next one - 4 berries, and so on, up to the oldest who got $2^{99}$ berries. A fox suggested they divide the berries "fairly." She can approach two bear cubs and distribute their berries equally between them, with any leftover berry being eaten by the fox. She continues this process until all the bear cubs have the same number of berries. What is the maximum number of berries that the fox can eat?

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