
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 plane $(xOy)$, points $A(2,2)$ and $B(0,4)$ are given. Circle $C$ has line segment $AB$ as its diameter.
(1) Find the equation of circle $C$.
(2) Let point $P$ be a point on circle $C$ that does not coincide with point $A$, and $OP=OA$. Find the equation of line $PA$ and the area of $\triangle POA$.

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