
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 $O$: $x^2+y^2=1$, and line $l$: $2x-y-4=0$. If point $A$ is on line $l$ such that there exists a point $B$ on circle $O$ and $\angle OAB=30^{\circ}$ (where $O$ is the origin), then the range of the $x$-coordinate of point $A$ is...

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