
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 a Circle \( C: (x-1)^{2}+(y- \sqrt {3})^{2}=1 \) and two points \( A(0,m) \), \( B(0,-m) \) (\( m > 0 \)), if there exists a point \( P \) on circle \( C \) such that \( \angle APB=90^{\circ} \), then the range of values for the real number \( m \) is ________.

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