
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
Determine the real numbers \( x \) that satisfy the equation

\[ 
\frac{1}{998} \cdot \left(\sqrt{2 \sqrt{2} x - x^{2} - 1} + \ldots + \sqrt{2 \sqrt{2} x - x^{2} + k^{2} - 2} + \ldots + \sqrt{2 \sqrt{2} x - x^{2} + 1995^{2} - 2}\right) = 1995
\]

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