
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 circle \\(C\\): \\((x-3)^{2}+(y-4)^{2}=1\\) and two points \\(A(-m,0)\\), \\(B(m,0)\\) where \\(m > 0\\). If there exists a point \\(P\\) on the circle such that \\(∠APB=90^{\circ}\\), then the range of values for \\(m\\) is \_\_\_\_\_\_.

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