
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
\[\frac{(\sqrt{3} - 1)^{1 - \sqrt{2}}}{(\sqrt{3} + 1)^{1 + \sqrt{2}}},\]
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