
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 domain of the function $f(x)$ is $D$, and $f(X)=\{y|y=f(x),x∈X⊆D\}$, $f^{-1}(Y)=\{x|f(x)∈Y,x∈D\}$. If $f(x)=2\sin (ωx+ \frac {5π}{6})(ω > 0)$, $D=\[0,π\]$, and $f(f^{-1}(\[0,2\])=\[0, 2\]\)$, find the range of $ω$.

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