
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]


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Let  $k$  and  $n$  be positive integers and let  $x_1, x_2, \cdots, x_k, y_1, y_2, \cdots, y_n$  be distinct integers. A polynomial  $P$  with integer coefficients satisfies
 \[P(x_1)=P(x_2)= \cdots = P(x_k)=54\] 
\[P(y_1)=P(y_2)= \cdots = P(y_n)=2013.\]

Determine the maximal value of  $kn$ .

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