
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
Given the function $f(x)= \frac{ax^2+1}{bx+c}$ is an odd function (where $a$, $b$, $c$ are constants),  
(1) Determine the value of the real number $c$.  
(2) If $a$ and $b$ are positive integers, and it is given that $f(1)=2$ and $f(2)<3$, find the explicit form of $f(x)$.  
(3) For the function $f(x)$ from part (2), if the equation $f(x)=m$ has positive solutions, determine the range of values for the real number $m$.

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