
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 plane $(xOy)$, the circle $x^{2}+y^{2}=1$ intersects the $x$-axis at points $A$ and $B$, with point $A$ to the left of point $B$. If there exists a point $P$ on the line $x+\sqrt{3}y+m=0$ such that $PA=2PB$, find the range of values for $m$.

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