
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 girl walks diagonally across a rectangular park, saving a distance equal to $\frac{1}{3}$ of the longer side compared to walking along the two adjacent sides. If the shorter side of the rectangle is half as long as the longer side, find the ratio of the longer side of the rectangle to the diagonal.
**A)** $\frac{2}{5}$  
**B)** $\frac{\sqrt{5}}{2}$  
**C)** $\frac{2\sqrt{5}}{5}$  
**D)** $\frac{5}{2}$  
**E)** $\frac{1}{2}$

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