
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

Simplify the following expressions:

$$
\frac{\frac{2x+1}{x+1} - \frac{2x-1}{x}}{\frac{2x-1}{x-1} - \frac{2x+1}{x}}
$$

$$
\frac{x^2 + x}{x^2 + 3x + 2} - \frac{x^2 - 3x + 2}{x^2 - x} + \frac{x^2 - 7x + 12}{x^2 - 5x + 6}
$$

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