
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 positive real numbers \( x \) and \( y \), let \( a=x+y \) and \( b=\sqrt{x^{2}+7xy+y^{2}} \).

(1) When \( y=1 \), find the range of values for \( \frac{b}{a} \).

(2) If \( c^{2} = k \cdot xy \), and for any positive numbers \( x \) and \( y \), segments with lengths \( a \), \( b \), and \( c \) can always form a triangle, determine the range of values for \( k \).

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