
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
Let $g$ be a function defined on the set of positive rational numbers with the property that $g(a\cdot b) = g(a) + g(b)$ for all positive rational numbers $a$ and $b$. Suppose $g$ has the property that $g(p) = p^2$ for every prime number $p$. For which of the following numbers $x$ is $g(x) \leq 0$?
1. $\frac{2}{5}$
2. $\frac{3}{25}$
3. $\frac{7}{49}$
4. $\frac{11}{121}$
5. $\frac{5}{4}$
A) $\frac{2}{5}, \frac{3}{25}, \frac{7}{49}, \frac{11}{121}$  
B) $\frac{3}{25}, \frac{7}{49}, \frac{11}{121}$  
C) $\frac{2}{5}, \frac{7}{49}, \frac{11}{121}$  
D) $\frac{11}{121}$ only  
E) None of the options

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