
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
Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system $xOy$, the parametric equation of line $l_1$ is $\begin{cases}x=2+t \\ y=kt\end{cases}$ (where $t$ is the parameter), and the parametric equation of line $l_2$ is $\begin{cases}x=-2+m \\ y= \frac{m}{k}\end{cases}$ (where $m$ is the parameter). Let the intersection point of $l_1$ and $l_2$ be $P$. When $k$ changes, the trajectory of $P$ is curve $C$.

(1) Write the general equation of $C$;

(2) Establish a polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis. Let line $l_3: \rho(\cos \theta +\sin \theta)− \sqrt{2} =0$, and $M$ be the intersection point of $l_3$ and $C$. Find the polar radius of $M$.

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