
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 the hyperbola $x^{2}- \frac {y^{2}}{3}=1$, with the left and right foci denoted as $F_{1}$ and $F_{2}$, respectively, determine the range of $r$ for the circle $(x-3)^{2}+y^{2}=r^{2}(r > 0)$ such that $\overrightarrow{PF_{1}}\cdot \overrightarrow{PF_{2}}=0$.

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