
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 $C$ with equation $(x-6)^{2}+(y-8)^{2}=1$ and two points $A(-m,0)$ and $B(m,0)$, where $m > 0$. For any point $P$ on the circle, $\angle APB < 90^{\circ}$. Determine the range of values for $m$.

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