
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
The line $y= \sqrt {3}x-m$ intersects the circle $x^{2}+y^{2}=9$ at two distinct points $M$ and $N$, and $| \overrightarrow {MN}| \geq \sqrt {6} | \overrightarrow {OM}+ \overrightarrow {ON}|$, where $O$ is the origin. The range of the real number $m$ is \_\_\_\_\_\_.

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