
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 \( x = \frac{1}{2}\left(1991^{\frac{1}{n}}-1991^{-\frac{1}{n}}\right) \) where \( n \) is a natural number, determine the value of \( \left(x - \sqrt{1 + x^2}\right)^n \).

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