
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
At a large round table facing the center, there are 55 people feasting: 25 barons, 20 counts, and 10 marquises. On signal, exactly those people should stand who have both their left and right neighbors with the same title. What is the maximum number of people that can stand?

For example, for a count to stand, both his neighbors must have the same title, but it does not necessarily need to be the title of a count.

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