
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
Point $P$ is any point on the line $y= \frac {3}{4}x$, with $F_{1}(-5,0)$ and $F_{2}(5,0)$. The range of values for $||PF_{1}|-|PF_{2}||$ is ______.

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