
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 Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases} x= \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t\end{cases}$ (where $t$ is the parameter), and the equation of circle $C$ is $x^{2}+y^{2}-4x-2y+4=0$. Establish a polar coordinate system with $O$ as the pole and the positive $x$-axis as the polar axis.  
$(1)$ Find the general equation of $l$ and the polar equation of $C$;  
$(2)$ Given that $l$ intersects $C$ at points $P$ and $Q$, find $|PQ|$.

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