
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
In the Cartesian coordinate system $xOy$, there are points $A(1,0)$ and $B(4,0)$. If there exists a point $P$ on the line $x-y+m=0$ such that $PA= \frac {1}{2}PB$, then the range of the real number $m$ is \_\_\_\_\_\_.

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