
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 square with side length $4$, a square is dissected into four pieces. Points $P$ and $Q$ are the midpoints of opposite sides, and line $CK$ is perpendicular to $DQ$. These four pieces when reassembled form a rectangle. Determine the ratio of the height to the base, $UV / VW$, in this new rectangle.
**A**. $\frac{1}{5}$  
**B**. $\frac{3}{5}$  
**C**. $\frac{4}{5}$  
**D**. $\frac{6}{5}$  
**E**. $\frac{7}{5}$

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