
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 $f(x)$ defined by the functional equation $f(x)-f(y)=f\left( \dfrac {x-y}{1-xy}\right)$ on $(-1,1)$, with $f(x) > 0$ when $x\in(-1,0)$, and $f\left(- \dfrac {1}{2}\right)=1$, determine the relationship between the real number $m=f\left( \dfrac {1}{5}\right)+f\left( \dfrac {1}{11}\right)+\ldots+f\left( \dfrac {1}{n^{2}+n-1}\right),\; n\geqslant 2,n\in\mathbb{N}^{*}$ and $-1$.

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