
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
1. (1) If \( x > 0 \), \( y > 0 \), \( z > 0 \), and \( x^{2} + y^{2} + z^{2} = 1 \), find the minimum value of \( \frac{x y}{z} + \frac{y z}{x} + \frac{z x}{y} \).
   
2. Given \( a, d \geq 0 \), \( b, c > 0 \), and \( b + c \geq a + d \), find the minimum value of \( \frac{b}{b + d} + \frac{c}{a + b} \).

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