
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 f be a function from  $\{1, 2, . . . , 22\}$  to the positive integers such that  $mn | f(m) + f(n)$  for all  $m, n \in \{1, 2, . . . , 22\}$ . If  $d$  is the number of positive divisors of  $f(20)$ , compute the minimum possible value of  $d$ .

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