
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 $\frac{a}{10^x-1}+\frac{b}{10^x+3}=\frac{3 \cdot 10^x+4}{(10^x-1)(10^x+3)}$ is an identity for positive rational values of $x$, then the value of $a-b$ is:
A) $\frac{1}{2}$  
B) $\frac{1}{4}$  
C) $\frac{3}{4}$  
D) $\frac{2}{3}$  
E) $\frac{1}{3}$

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