
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
In $\triangle ABC$, $\angle C= \frac{\pi}{2}$, $\angle B= \frac{\pi}{6}$, and $AC=2$. $M$ is the midpoint of $AB$. $\triangle ACM$ is folded along $CM$ such that the distance between $A$ and $B$ is $2\sqrt{2}$. The surface area of the circumscribed sphere of the tetrahedron $M-ABC$ is \_\_\_\_\_\_.

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