
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
Bessie and her  $2015$  bovine buddies work at the Organic Milk Organization, for a total of  $2016$  workers. They have a hierarchy of bosses, where obviously no cow is its own boss. In other words, for some pairs of employees  $(A, B)$ ,  $B$  is the boss of  $A$ . This relationship satisfies an obvious condition: if  $B$  is the boss of  $A$  and  $C$  is the boss of  $B$ , then  $C$  is also a boss of  $A$ . Business has been slow, so Bessie hires an outside organizational company to partition the company into some number of groups. To promote growth, every group is one of two forms. Either no one in the group is the boss of another in the group, or for every pair of cows in the group, one is the boss of the other. Let  $G$  be the minimum number of groups needed in such a partition. Find the maximum value of  $G$  over all possible company structures.

*Proposed by Yang Liu*

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