
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 the equation $x^2+y^2+(\sqrt{3}t+1)x+ty+t^2-2=0$ represents a circle.  
(1) Find the range of values for $t$;  
(2) If the diameter of the circle is 6, find the value of $t$.

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