
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 \( \triangle ABC \), \(\angle C = 90^\circ\), \(\angle B = 30^\circ\), \(AC = 2\). \(M\) is the midpoint of \(AB\). Fold \(\triangle ACM\) along \(CM\) such that the distance between points \(A\) and \(B\) is \(2\sqrt{2}\). Find the volume of the triangular prism \(A-BCM\) formed in this manner.

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