
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 rectangle has a length to width ratio of $5:2$. The perimeter of this rectangle is $42$ cm, and it has a diagonal $d$. Express the area $A$ of the rectangle in terms of $d$ as $kd^2$ for some constant $k$. What is $k$?
**A)** $\frac{12}{29}$
**B)** $\frac{10}{25}$
**C)** $\frac{11}{28}$
**D)** $\frac{10}{29}$
**E)** $\frac{9}{29}$

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