
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 $(xOy)$, a circle $⊙O$ with equation $x^{2}+y^{2}=4$ and a line $l$: $x=4$ are given. In the polar coordinate system with the pole at $O$ and the positive semi-axis on the $x$-axis, let a ray emanate from the pole, intersecting $⊙O$ at $A$ and line $l$ at $B$.
(1) Write the polar coordinate equations for $⊙O$ and line $l$;
(2) Let $M$ be the midpoint of $AB$. Find the trajectory equation of moving point $M$.

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