
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 $\varphi(n)$ denote the number of positive integers not exceeding $n$ that are coprime to $n$, and let $g(n)$ satisfy the condition that for any $n \in \mathbf{Z}_{+}$, $\sum_{d \| n} g(d)=\varphi(n)$, where $\sum_{d \| n}$ indicates the sum over all positive divisors of $n$. 
Find $g(50)$.




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