
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 $(xOy)$, a circle $O: x^2 + y^2 = 4$ and a line $l: y = x - 3$ are given. $P$ is a point on line $l$. If a circle with radius $1$ centered at point $P$ intersects circle $O$, what is the range of possible x-coordinate values for point $P$?

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