
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
Consider the identity $\frac{a}{10^{x+1}-1}+\frac{b}{10^{x+1}+3}=\frac{3 \cdot 10^x + 4}{(10^{x+1}-1)(10^{x+1}+3)}$ for positive rational values of $x$. Determine the value of $a - b$.
A) $\frac{37}{20}$
B) $\frac{43}{40}$
C) $\frac{51}{25}$
D) $\frac{31}{15}$
E) $\frac{1}{2}$

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