
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
After learning fractional operations, the teacher gave a question: "Calculate $ \dfrac{2x}{x^{2}-1}- \dfrac{1}{x-1}$." Xiao Ming's solution is as follows:

The original expression $= \dfrac{2x}{\left(x+1\right)\left(x-1\right)}- \dfrac{x+1}{\left(x+1\right)\left(x-1\right)}      \ldots \ldots $ Step 1

$=2x-\left(x+1\right)\ldots \ldots $ Step 2

$=2x-x-1       \ldots \ldots $ Step 3

$=x-1          \ldots \ldots $ Step 4

(1) The error in the above solution process starts from step 2;

(2) When $x$ is a positive integer solution to $x-3 \lt 0$, find the value of $ \dfrac{2x}{x^{2}-1}- \dfrac{1}{x-1}$.

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