
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 fish shop with 28 kinds of fish, there are 28 fish sellers. In every seller, there exists only one type of each fish kind, depending on where it comes, Mediterranean or Black Sea. Each of the  $k$  people gets exactly one fish from each seller and exactly one fish of each kind. For any two people, there exists a fish kind which they have different types of it (one Mediterranean, one Black Sea). What is the maximum possible number of  $k$ ?

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