
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, 90 people are feasting: 40 barons, 30 counts, and 20 marquises, all facing the center of the table. At a signal, exactly those who have both neighbors (left and right) with the same title should stand up. What is the maximum number of people who can stand up? 

For example, in order for a count to stand up, both of their neighbors must have the same title, though not necessarily the title of count.

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