
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
(1) Solve the equation: $\frac{1}{x-1}+1=\frac{3}{2x-2}$;<br/>(2) Simplify first, then find the value: $(\frac{x^2}{1+x}-x)÷\frac{x^2-1}{x^2+2x+1}$, where $x=\frac{1}{2}$.

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