
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 the circle $C$ passes through the origin $O$ and the point $(4,0)$, with its center lying on the $x$-axis.<br/>$(1)$ Find the equation of circle $C$;<br/>$(2)$ Given that the line $l:3x+4y-11=0$ intersects circle $C$ at points $A$ and $B$, find the length of the chord $|AB|$.

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