
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
Find the equations of the tangent lines to the circle $x^2+y^2=4$ under the following conditions:  
(1) Passing through point $P(\sqrt{3},1)$, (2) Passing through point $Q(3,0)$, (3) Having a slope of $-1$.

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