
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
Evaluate the arithmetic mean between \( \frac{x + a + b}{x + b} \) and \( \frac{x - a - b}{x - b} \), where \( x, a, b \) are such that \( x \neq \pm{b} \).
**A)** \( 1 \)  
**B)** \( 1 - \frac{ab}{x^2 - b^2} \)  
**C)** \( 1 + \frac{ab}{x^2 - b^2} \)  
**D)** \( 1 - \frac{a^2 - b^2}{x^2} \)

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