
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
Let $a$ and $b$ be lengths of two line segments where $a = 2x$ and $b = 2x^2$ with $x > 0$. Find the exact value of the arithmetic mean and the geometric mean.
**A)** AM = $x^2 - x$, GM = $x^{1.5}$  
**B)** AM = $x + x^2$, GM = $2x^{1.5}$  
**C)** AM = $2x + x^2$, GM = $2x^2$  
**D)** AM = $x^2 + 2x$, GM = $x^{1.5}$

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