
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
Find all values of $x$ for which:
\[\frac{8}{\sqrt{x - 5} - 10} + \frac{2}{\sqrt{x - 5} - 5} + \frac{10}{\sqrt{x - 5} + 5} + \frac{16}{\sqrt{x - 5} + 10} = 0.\]

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