
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 triangle $ABC$ with vertex coordinates $A(0,1)$, $B(-\sqrt{3},0)$, $C(\sqrt{3},0)$, let circle $M$ be the circumscribed circle of $\triangle ABC$.
(Ⅰ) Find the standard equation of circle $M$.
(Ⅱ) Line $l$ passes through the point $(1,3)$ and intersects circle $M$ at points $P$ and $Q$. The length of chord $PQ$ is $2\sqrt{3}$. Find the equation of line $l$.

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