
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 Cartesian coordinate system $(xOy)$, a line $l$ passes through the fixed point $Q(1,1)$ and intersects the curve $C$: $y=\frac{x}{x-1}$ at points $M$ and $N$. Calculate the value of $\overrightarrow{ON} \cdot \overrightarrow{OQ} - \overrightarrow{MO} \cdot \overrightarrow{OQ}$.

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