
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
What is the sum of all possible values of s between 0 and 360 such that the triangle in the coordinate plane whose vertices are in the terms of cosine and sine of the angles s, 90, and 30 is an isosceles right triangle?

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