
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
The 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 are satisfied:
\[ f(n a, n b, n c) = n \cdot f(a, b, c) \]
\[ f(a+n, b+n, c+n) = f(a, b, c) + n \]
\[ f(a, b, c) = f(c, b, a) \]
Find \( f(24, 25, 26) \).

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