
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
Given a moving point $M(x,y)$, the ratio of its distance to the fixed point $A(1,0)$ and to the straight line $l: x=4$ is $\frac{1}{2}$.
1. Find the equation of the trajectory $C$ of point $M$.
2. A line passing through point $N(-1,1)$ intersects the curve $C$ at points $P$ and $Q$, with $N$ being the midpoint of the line segment $PQ$. Find the equation of line $PQ$.

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