
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 points $O(0,0)$, $A(2,0)$, $B(2,2)$.  
$(1)$ Find the standard equation of the circle $M$ passing through points $O$, $A$, and $B$.  
$(2)$ The equation of the line $l$ is $y=x-1$. The line intersects the circle $M$ at points $P$ and $Q$. Find the length of the chord $PQ$.

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