
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 triangle in the coordinate plane whose vertices are $(\cos 30^\circ,\sin 30^\circ), (\cos 90^\circ,\sin 90^\circ),$ and $(\cos t^\circ,\sin t^\circ)$ is isosceles without overlapping any points, find the sum of all possible values of $t$ between $0$ and $360$.

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