
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
\[ g(x^2 y) = 2g(x) + g(y) \]
for all positive integers \(x\) and \(y\). Given \(g(5) = 4\) and \(g(20) = 10\), find \(g(200)\).

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