
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 \(\frac{a}{10^x-1}+\frac{b}{10^x+2}=\frac{3 \cdot 10^x + 5}{(10^x-1)(10^x+2)}\) holds as an identity for positive rational values of \(x\), calculate \(a-b\).

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