
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 the function $f(x)=\sin (ωx+φ)(ω > 0,0 < φ < π)$ with a period of $4$, the graph of the function $f(x)$ is shifted to the right by $\frac{1}{3}$ unit, and the resulting graph is symmetric about the origin. Determine the range of the function $y=f(x)$ on the interval $[0,1]$.

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