
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
Determine the sum of all possible values of $t$ between $0$ and $360$ degrees such that the triangle in the coordinate plane with vertices at \[(\cos 30^\circ, \sin 30^\circ), (\cos 90^\circ, \sin 90^\circ), \text{ and } (\cos t^\circ, \sin t^\circ)\] is isosceles.
A) 660 
B) 690 
C) 720 
D) 750 
E) 800

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