
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
Let \( g \) be a function defined on the positive integers, such that 
\[ g(xy) = g(x) + g(y) \]
for all positive integers \( x \) and \( y \). Given \( g(15) = 18 \) and \( g(45) = 24 \), find \( g(675) \).

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