
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
Find the sum of   $$ \frac{\sigma(n) \cdot d(n)}{ \phi (n)} $$   over all positive  $n$  that divide  $ 60$ .

Note: The function  $d(i)$  outputs the number of divisors of  $i$ ,   $\sigma (i)$  outputs the sum of the factors of  $i$ , and  $\phi  (i)$  outputs the number of positive integers less than or equal to  $i$  that are relatively prime to  $i$ .

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