
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
Simplify the expression
\[
\frac{(\sqrt{2} - 1)^{2 - \sqrt{3}}}{(\sqrt{2} + 1)^{2 + \sqrt{3}}},
\]
writing your answer as \(a - b \sqrt{c},\) where \(a,\) \(b,\) and \(c\) are positive integers, and \(c\) is not divisible by the square of a prime.

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