
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
A rhombus has one diagonal that is twice the length of the other diagonal. If the shorter diagonal is $12$ inches, express the side length of the rhombus in terms of $L$, where $L$ is the area of the rhombus in square inches.
A) $6\sqrt{5}$ inches
B) $12\sqrt{5}$ inches
C) $18\sqrt{5}$ inches
D) $24\sqrt{5}$ inches

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