
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
In a certain kingdom, there were 32 knights. Some of them were vassals of others (a vassal can have only one liege, and a liege is always wealthier than their vassal). A knight with at least four vassals held the title of baron. What is the maximum number of barons that could exist under these conditions?

(In the kingdom, the law stated: "a vassal of my vassal is not my vassal.")

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