
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 long side \( b \) and a short side \( a \). The ratio \( \frac{a}{b} \) is such that \( \tan(\theta) = \frac{a}{b} \), where \( \theta \) is an angle such that \( \cos(\theta) = \frac{3}{5} \) and \( \theta \) is acute. Given this information, what is the ratio \( k^2 = \left(\frac{a}{b}\right)^2 \)?
A) \(\frac{9}{16}\)
B) \(\frac{8}{9}\)
C) \(\frac{16}{9}\)
D) \(\frac{25}{9}\)

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