
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
Given is a prime number  $p$  and natural  $n$  such that  $p \geq n \geq 3$ . Set  $A$  is made of sequences of lenght  $n$  with elements from the set  $\{0,1,2,...,p-1\}$  and have the following property:
  For arbitrary two sequence  $(x_1,...,x_n)$  and  $(y_1,...,y_n)$  from the set  $A$  there exist three different numbers  $k,l,m$  such that:

 $x_k \not = y_k$ ,  $x_l \not = y_l$ ,  $x_m \not = y_m$ .
Find the largest possible cardinality of  $A$ .

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