
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
Three straight lines \( y=\sqrt{2} x \), \( y=-\sqrt{2} x \), and \( x=m \) divide the ellipse \(\frac{x^{2}}{4}+y^{2} \leqslant 1\) into several regions. Each region is colored with one of 6 different colors, and no two adjacent regions have the same color. There are a total of 720 ways to color the regions. Determine the range of the real number \( m \).

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