
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
\[
\frac{(\sqrt{3} - 1)^{2 - \sqrt{5}}}{(\sqrt{3} + 1)^{2 + \sqrt{5}}},
\]
writing your answer as $p - q \sqrt{r},$ where $p,$ $q,$ and $r$ are positive integers, and $r$ is not divisible by the square of a prime.

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