
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 $n$. Let $g(n)$ satisfy that for any $n \in \mathbf{N}_{+}$, $\sum_{d \mid n} g(d) = \varphi(n)$, where the summation symbol $\sum_{d \mid n}$ denotes that $d$ ranges over all positive divisors of $n$. Find $g(50)$.

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