
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 any positive integer  $n$ , let  $D_n$  denote the set of all positive divisors of  $n$ , and let  $f_i(n)$  denote the size of the set   $$ F_i(n) = \{a \in D_n | a \equiv i \pmod{4} \} $$  where  $i = 1, 2$ .
Determine the smallest positive integer  $m$  such that  $2f_1(m) - f_2(m) = 2017$ .

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