
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 the ellipse $M: \frac{x^{2}}{m}+ \frac{y^{2}}{3}=1(m>3)$, $M$ intersects with two lines $y=kx$, $y=-kx$ ($k≠0$) at four different points. These four points and the two foci of $M$ form a regular hexagon. Find $m$.

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