
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 circle $C$ passes through points $A(2,0)$ and $B(0,4)$, and the center of the circle lies on the line $2x-y-3=0$.
$(1)$ Find the standard equation of circle $C$;
$(2)$ The line $l$ passing through point $T(-1,0)$ intersects circle $C$ at points $P$ and $Q$, and $\overrightarrow{CP}•\overrightarrow{CQ}=-5$. Find the equation of line $l$.

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