
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
Let \( x_{1} \) and \( x_{2} \) be the roots of the equation \( \sqrt{14} x^{2}-\sqrt{116} x+\sqrt{56}=0 \). Calculate \( \left|\frac{1}{x_{1}^{2}}-\frac{1}{x_{2}^{2}}\right| \).

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