
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 positive integer \( n \), denote by \( \tau(n) \) the number of positive integer divisors of \( n \), and denote by \( \phi(n) \) the number of positive integers that are less than or equal to \( n \) and relatively prime to \( n \). Call a positive integer \( n \) good if \( \phi(n) + 4 \tau(n) = n \). For example, the number 44 is good because \( \phi(44) + 4 \tau(44) = 44 \). Find the sum of all good positive integers \( n \).

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