
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 the function \( y = y_1 + y_2 \), where \( y_1 \) is directly proportional to \( x^2 \) and \( y_2 \) is inversely proportional to \( x^2 \). When \( x = 1 \), \( y = 5 \); when \( x = \sqrt{3} \), \( y = 7 \). Find the value of \( x \) when \( y \) is minimized.

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