
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
In the homework assigned by the teacher, there is a fractional calculation problem: $\frac{2}{x+1}-\frac{x+5}{x^2-1}$. Two students, A and B, completed the process as follows:<br/>$(1)$ The teacher found errors in the answers of these two students. Student A made a mistake starting from step______; student B made a mistake starting from step______;<br/>$(2)$ Please rewrite the correct solution process for this question.<br/><table><tbody><tr><td width="426">Student A</td><td width="426">Student B</td></tr><tr><td align="left">$\frac{2}{x+1}-\frac{x+5}{{x}^{2}-1}$<br/>$=\frac{2(x-1)}{(x+1)(x-1)}-\frac{x+5}{(x+1)(x-1)}$Step 1<br/>$=\frac{2x-2-x+5}{(x+1)(x-1)}$Step 2<br/>$=\frac{x+3}{(x+1)(x-1)}$Step 3</td><td align="left">$\frac{2}{x+1}-\frac{x+5}{{x}^{2}-1}$<br/>$=\frac{2(x-1)}{(x+1)(x-1)}-\frac{x+5}{(x+1)(x-1)}$Step 1<br/>$=2x-2-x-5 $Step 2<br/>$=x-7 $Step 3</td></tr></tbody></table>

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