
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
Suppose \( x = \frac{13}{\sqrt{19 + 8 \sqrt{3}}} \). Find the exact value of
\[ 
\frac{x^{4} - 6 x^{3} - 2 x^{2} + 18 x + 23}{x^{2} - 8 x + 15}.
\]

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