
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
Read the following solution process and answer the question. Calculate: $\frac{x-5}{x-3}-\frac{{x}^{2}+2x+1}{{x}^{2}+x}÷\frac{x+1}{x-2}$. Solution: Original expression $=\frac{x-5}{x-3}-\frac{(x+1)^{2}}{x(x+1)}•\frac{x-2}{x+1}$ $=\frac{x-5}{x-3}-\frac{x-2}{x}$ $=\frac{x(x-5)}{x(x-3)}-\frac{(x-2)(x-3)}{x(x-3)}$ $=\frac{{x}^{2}-5x-{x}^{2}-5x+6}{x(x-3)}$ $=\frac{-10x+6}{x(x-3)}$ Is the above solution process correct? If not, please write down the correct solution process.

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