
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 \( g \) 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: \( g(n a, n b, n c) = n \cdot g(a, b, c) \), \( g(a+n, b+n, c+n) = g(a, b, c) + n \), \( g(a, b, c) = g(c, b, a) \). Find \( g(14, 15, 16) \).

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