
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 took a shortcut along the diagonal of a rectangular park, saving a distance equal to $\frac{1}{3}$ the length of the longer side of the rectangle. If the shorter side of the rectangle is $\frac{1}{3}$ the length of the longer side, determine the ratio of the length of the diagonal to the perimeter of the rectangle.
A) $\frac{\sqrt{10}}{8}$
B) $\frac{\sqrt{10}}{9}$
C) $\frac{\sqrt{10}}{7}$
D) $\frac{3\sqrt{10}}{8}$

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