
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, defined on the set of positive integers, is such that \( f(x y) = f(x) + f(y) \) for all \( x \) and \( y \). It is known that \( f(10) = 14 \) and \( f(40) = 20 \).

What is the value of \( f(500) \)?

A) 29
B) 30
C) 39
D) 48
E) 50

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