
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 points $A( \frac {π}{6}, \frac { \sqrt {3}}{2}))$, $B( \frac {π}{4},1)$, and $C( \frac {π}{2},0)$, if these three points are all on the graph of the function $f(x)=\sin ωx$, then the set of all possible values for the positive number $ω$ is _______.

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