
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
Find all real values of  $ x>1$  which satisfy:

 $ \frac{x^2}{x\minus{}1} \plus{} \sqrt{x\minus{}1}  \plus{}\frac{\sqrt{x\minus{}1}}{x^2} \equal{} \frac{x\minus{}1}{x^2} \plus{} \frac{1}{\sqrt{x\minus{}1}} \plus{} \frac{x^2}{\sqrt{x\minus{}1}}$ 

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