
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
Zhiqiang, a student, discovered a series of equations in his extracurricular research:
\\(\dfrac{1 + \left(\frac{1}{2}\right)^2}{1 + 2^2} = \left(\dfrac{1 + \frac{1}{2}}{1 + 2}\right)^2\\),
\\(\dfrac{1 + 4^3}{1 + \left(\frac{1}{4}\right)^3} = \left(\dfrac{1 + 4}{1 + \frac{1}{4}}\right)^3\\),
\\(\dfrac{1 + \left(-\frac{\sqrt{2}}{2}\right)^4}{1 + (-\sqrt{2})^4} = \left(\dfrac{1 - \frac{\sqrt{2}}{2}}{1 - \sqrt{2}}\right)^4\\),
$\dots$
He wants to represent this pattern symbolically, and he has written part of it. Help him complete it. If $a$, $b \in \mathbb{R}$, $b \neq 1$, $ab = 1$, and $n \in \mathbb{N}^*$, then $\_\_\_\_\_\_$.

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