
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 $O$: $x^{2}+y^{2}=3$, line $l$: $x+3y-6=0$, and point $P(x_{0},y_{0})∈l$. If there exists a point $Q$ on circle $O$ such that $∠OPQ=60^{\circ}$, determine the range of $x_{0}$.

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