
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 $f$ be a function defined on the positive integers, such that
\[f(xy) = f(x) + f(y)\]
for all positive integers $x$ and $y.$ Given $f(10) = 16$, $f(40) = 24$, and $f(3) = 5$, find $f(800)$.

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