
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 $C$: $x^{2}+y^{2}=1$, point $P(x_{0},y_{0})$ is on line $x-y-2=0$, $O$ is the coordinate origin. If there exists a point $Q$ on circle $C$ such that $\angle OPQ=30^{\circ}$, then the range of $x_{0}$ is _____.

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