
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
Given a rectangle where the ratio of the length to the width is 5:2, and the rectangle has diagonal of length \(d\), find the constant \(k\) such that the area of the rectangle can be expressed as \(kd^2\).
**A)** \(\frac{10}{49}\)  
**B)** \(\frac{10}{25}\)  
**C)** \(\frac{10}{29}\)  
**D)** \(\frac{5}{14}\)  
**E)** \(\frac{20}{29}\)

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