
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
Famous mathematicians such as Rømer, Bernoulli's family, Leibniz, etc., have successively studied the properties of the star-shaped curve $C:{x^{\frac{2}{3}}}+{y^{\frac{2}{3}}}=1$. This curve is aesthetically pleasing and is commonly used in the design of ultra-light materials. The range of values for the distance from a moving point on curve $C$ to the origin is ____.

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