
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 Cartesian coordinate system $xOy$, and the polar axis is the positive half-axis of $x$, the unit of length is the same in both coordinate systems. The equation of the circle $C$ in the Cartesian coordinate system is $x^2 + y^2 + 2x - 2y = 0$, the parametric equation of the line $l$ is $\begin{cases} x=-1+t\\ y=t \end{cases}$ (where $t$ is the parameter), the polar equation of the ray $OM$ is $\theta = \frac{3\pi}{4}$.
(Ⅰ) Determine the polar equations for the circle $C$ and the line $l$.
(Ⅱ) It is known that the ray $OM$ intersects the circle $C$ at points $O$ and $P$, and intersects the line $l$ at point $Q$. Calculate the length of the line segment $PQ$.

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