
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 function \( f \) defined on the set of positive rational numbers satisfying \( f(a \cdot b) = f(a) \cdot f(b) \) for all \( a \) and \( b \), where \( f(x) = x^2 \) for every prime number \( x \). Determine \( f(x) \) where \( x = \frac{18}{49} \).
A) \( \frac{324}{2401} \)
B) \( \frac{324}{49} \)
C) \( \frac{18}{2401} \)
D) \( \frac{81}{49} \)

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