
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
Five identical empty buckets with a capacity of \( b \) liters each are placed at the vertices of a regular pentagon. In each round of the following game, the Stepmother takes one liter of water from the river and distributes it among the five buckets in any manner she chooses. Subsequently, Cinderella selects a pair of adjacent buckets, empties them into the river, and resets them to empty. The process repeats round by round. The Stepmother aims to make one of the buckets overflow with water, while Cinderella's objective is to prevent any bucket from overflowing. Determine all capacities \( b \) for which the Stepmother can inevitably cause a bucket to overflow.

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