
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
A function \( g: \mathbb{N} \rightarrow \mathbb{N} \) satisfies the following:
(a) If \( m \) is a proper divisor of \( n \), then \( g(m) < g(n) \).
(b) If \( m \) and \( n \) are relatively prime and greater than 1, then
\[ g(m n) = g(m) g(n) + (n+1) g(m) + (m+1) g(n) + m + n. \]

Find the least possible value of \( g(2016) \).

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