
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 vectors $\overrightarrow{a}=(a_{1},a_{2})$ and $\overrightarrow{b}=(b_{1},b_{2})$, define a kind of vector product $\overrightarrow{a}⊗\overrightarrow{b}=(a_{1}b_{1},a_{2}b_{2})$. Known vectors $\overrightarrow{m}=(2,\frac{1}{2})$ and $\overrightarrow{n}=(\frac{π}{3},0)$, point $P(x,y)$ moves on the graph of $y=\sin x$, and point $Q$ is on the graph of the function $y=f(x)$, satisfying $\overrightarrow{OQ}=\overrightarrow{m}⊗\overrightarrow{OP}+\overrightarrow{n}$ (where $O$ is the coordinate origin). Find the range of the function $y=f(x)$.

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