
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 that the pole of the polar coordinate system is the origin of the plane Cartesian coordinate system $xOy$, and the polar axis is the positive half-axis of $x$, the curve $C$ has the parametric equation $\begin{cases} x=-1+ \sqrt {2}\cos \alpha \\ y=1+ \sqrt {2}\sin \alpha\end{cases}$ (where $\alpha$ is the parameter), the line $l$ passes through the point $(-1,0)$, and its slope is $\dfrac {1}{2}$, the polar equation of the ray $OM$ is $\theta= \dfrac {3\pi}{4}$.
$(1)$ Find the polar equations of curve $C$ and line $l$;
$(2)$ Given that the ray $OM$ intersects the circle $C$ at points $O$ and $P$, and intersects line $l$ at point $Q$, find the length of segment $PQ$.

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