
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 that the triangle in the coordinate plane with vertices $(\cos 45^{\circ}, \sin 45^{\circ})$, $(\cos 90^{\circ}, \sin 90^{\circ})$, and $(\cos \theta^{\circ}, \sin \theta^{\circ})$ is isosceles, calculate the sum of all possible values of $\theta$ between $0$ and $360$.

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