
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 point \((a, b)\) moves on the curve \(\arcsin x = \arccos y\), and the ellipse \(a x^{2} + b y^{2} = 1\) is external to the circle \(x^{2} + y^{2} = \frac{2}{\sqrt{3}}\) (including the case where they are tangent), then the range of values for \(\arcsin b\) is \(\qquad\).

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