
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
For a given positive integer \( n \), we define \(\varphi(n)\) to be the number of positive integers less than or equal to \( n \) which share no common prime factors with \( n \). Find all positive integers \( n \) for which
$$\varphi(2019 n) = \varphi\left(n^{2}\right).$$

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