
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
Define the length of the interval $[x_{1},x_{2}]$ as $x_{2}-x_{1}$ ($x_{2} > x_{1}$), which is monotonically increasing. The function $f(x)= \dfrac {(a^{2}+a)x-1}{a^{2}x}$ ($a\in\mathbb{R},a\neq 0$) has both its domain and range as $[m,n]$ ($n > m$). When the interval $[m,n]$ reaches its maximum length, find the value of the real number $a$.

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