
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 a circle $O: x^{2}+y^{2}=4$ and a line $l: x+y-4=0$, let $A$ be a point on line $l$. If there exist two points $B$ and $C$ on circle $O$ such that $\angle BAC=60^{\circ}$, then the range of the x-coordinate of point $A$ is ______.

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