
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 $\frac{a}{10^x-2} + \frac{b}{10^x+3} = \frac{3 \cdot 10^x + 4}{(10^x-2)(10^x+3)}$ is an identity for positive rational values of $x$, find the value of $3a - 2b$.
A) 4
B) 5
C) 6
D) 3
E) 2

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