
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
When \( x \) takes positive rational numbers, if
$$
\frac{a}{10^{x}-1}+\frac{b}{10^{x}+2}=\frac{2 \cdot 10^{x}+3}{\left(10^{x}-1\right)\left(10^{x}+2\right)}
$$
is an identity, find the value of \( a - b \).

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