
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
The ratio of the length to the width of a rectangle is $5$ : $2$. If the perimeter of the rectangle is $42$ units, find the area expressed as $kd^2$, where $d$ is the length of the diagonal of the rectangle.
**A)** $\frac{10}{29}$  
**B)** $\frac{12}{25}$  
**C)** $\frac{15}{29}$  
**D)** $\frac{20}{29}$

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