
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 square with side length $4$ is dissected where $J$ and $K$ are midpoints of opposite sides, and $CD$ is perpendicular to $JK$. The pieces are rearranged into a triangle. Calculate the ratio of the smaller leg to the larger leg of this triangle.
A) $\frac{2}{5}$
B) $\frac{10}{\sqrt{5}}$
C) $\frac{2\sqrt{5}}{5}$
D) $\frac{5}{2\sqrt{5}}$
E) $\frac{\sqrt{5}}{2}$

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