
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 right focus F of the ellipse C: \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a>b>0) and a point N(0, \sqrt{2}b), let M be a moving point on C. If the maximum perimeter of \triangle MNF is (\sqrt{6}+2)a, find the eccentricity of C.

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