<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 A function \( F \) is defined on the set of triples of integers and takes real values. It is known that for any four integers \( a, b, c \), and \( n \), the following equalities hold: 
\[ 
F(n a, n b, n c) = n \cdot F(a, b, c), \\
F(a + n, b + n, c + n) = F(a, b, c) + n, \\
F(a, b, c) = F(c, b, a). 
\]
Find \( F(58, 59, 60) \). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
59
A function \( F \) is defined on the set of triples of integers and takes real values. It is known that for any four integers \( a, b, c \), and \( n \), the following equalities hold: 
\[ 
F(n a, n b, n c) = n \cdot F(a, b, c), \\
F(a + n, b + n, c + n) = F(a, b, c) + n, \\
F(a, b, c) = F(c, b, a). 
\]
Find \( F(58, 59, 60) \).
test