
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 $(xOy)$, line $l$ passes through point $M(3,4)$ with a slope angle of $45^{\circ}$. The parametric equations of circle $C$ are given by $\begin{cases} x=2\cos \theta \ y=2+2\sin \theta \end{cases} (\theta \text{ is the parameter})$. Establish a polar coordinate system with the origin as the pole, the positive $x$-axis as the polar axis, and with the same length unit as the rectangular coordinate system $(xoy)$.
(1) Find the polar equation of circle $C$.
(2) If circle $C$ intersects line $l$ at points $A$ and $B$, find the value of $|MA| \cdot |MB|$.

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