
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 $C: x^2 + y^2 = 1$, and point $P(x_0, y_0)$ is on the line $l: 3x + 2y - 4 = 0$. If there always exist two different points $A, B$ on circle $C$ such that $\vec{OA} + \vec{OB} = \vec{OP}$, then the range of values for $x_0$ is ______.

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