
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: $x^2+y^2=4$ and a point P $(x_0, y_0)$ outside circle O. Two tangents to circle O are drawn from point P, touching the circle at points A and B, respectively, and $\angle AOB=120^\circ$. If point C $(6,0)$ and point P satisfy $PO=\lambda PC$, then the range of $\lambda$ is \_\_\_\_\_\_.

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