
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 $5$ : $2$. If the rectangle has a diagonal of length $d$, what is the coefficient $k$ such that the area of the rectangle, $A$, can be expressed as $A = kd^2$?
**A)** $\frac{10}{29}$  
**B)** $\frac{8}{29}$  
**C)** $\frac{12}{29}$  
**D)** $\frac{15}{29}$

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