
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
Let vectors $\overrightarrow{a} = (a_1, a_2)$, $\overrightarrow{b} = (b_1, b_2)$, and define a vector product $\overrightarrow{a} \otimes \overrightarrow{b} = (a_1b_1, a_2b_2)$. Given vectors $\overrightarrow{m} = (2, \frac{1}{2})$, $\overrightarrow{n} = (\frac{\pi}{3}, 0)$, and point P(x, y) moves on the graph of $y=\sin x$. Point Q is on the graph of function $y=f(x)$, and satisfies $\overrightarrow{OQ} = \overrightarrow{m} \otimes \overrightarrow{OP} + \overrightarrow{n}$ (where O is the origin). Find the range of the function $y=f(x)$.

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