
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 rectangular coordinate system $(xOy)$, the parametric equation of line $l\_1$ is $\begin{cases} x=2+t \ y=kt \ \end{cases}$ ($t$ is the parameter), and the parametric equation of line $l\_2$ is $\begin{cases} x=-2+m \ y=\frac{m}{k} \ \end{cases}$ ($m$ is the parameter). Let $P$ be the intersection point of $l\_1$ and $l\_2$, and curve $C$ be the trajectory of $P$ when $k$ varies.
(1) Write the ordinary equation of $C$;
(2) Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. Let $l\_3$ be the line represented by $ρ(cos⁡θ+sin⁡θ)-\sqrt{2}=0$, and $M$ be the intersection point of $l\_3$ and $C$. Calculate the polar radius of $M$.

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