
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
Find all numbers \( k \) for which

\[ 
\left(\frac{k}{2}\right)!\left(\frac{k}{4}\right) = 2016 + k^2 
\]

The symbol \( n! \) denotes the factorial of the number \( n \), that is, the product of all integers from 1 to \( n \) inclusive (defined only for non-negative integers; \( 0! = 1 \) ).

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