
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
Given that the real numbers \( x, a_{1}, a_{2}, y \) form an arithmetic sequence, and the real numbers \( x, b_{1}, b_{2}, y \) form a geometric sequence, find the value range of \( \frac{(a_{1} + a_{2})^{2}}{b_{1} b_{2}} \).

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