
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
In a rhombus where one diagonal is three times the length of the other diagonal, determine the expression for the side of the rhombus in terms of its area $K$ (in square units).
A) \( \sqrt{\frac{2K}{3}} \)
B) \( \sqrt{\frac{5K}{3}} \)
C) \( \sqrt{\frac{5K}{6}} \)
D) \( \sqrt{\frac{9K}{4}} \)
E) \( \sqrt{\frac{12K}{5}} \)

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