
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 \( n \). Define \( f_i(n) (i=1,2) \) as the number of elements in the set
\[ F_i(n) = \{ a \in D_n \mid a \equiv i \pmod{4} \} \]
Find the smallest positive integer \( m \) such that
\[ 2f_1(m) - f_2(m) = 2017. \]

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