
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
Find the roots of the equation $4\sqrt{x} + 3x^{-\frac{1}{2}} = 10$.
**A)** \( x = \frac{19 + 5\sqrt{13}}{8} \text{ only} \) \
**B)** \( x = \frac{19 - 5\sqrt{13}}{8} \text{ only } \) \
**C)** \( x = \frac{19 + 5\sqrt{13}}{8} \text{ and } x = \frac{19 - 5\sqrt{13}}{8} \) \
**D)** \( x = 0.75 \text{ or } x = 0.25 \) \
**E)** None of the above.

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