
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
If $b>1$, $x>0$, and $(3x)^{\log_b 3}-(5x)^{\log_b 5}=0$, then $x$ is which of the following?
A) $\frac{1}{15}$
B) $\frac{1}{5^{\log_{\frac{5}{3}} b}}$
C) $\frac{1}{10}$
D) $1$
E) $\frac{1}{5}$

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