
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 $A(-m,0)$, $B(m,0) (m > 0)$. Find the range of values for $m$ such that there exists a point $P$ on the circle such that $\overrightarrow{PA} \cdot \overrightarrow{PB}=0$.

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