
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 \( \triangle ABC \), \( \angle C=90^\circ \), \( \angle B=30^\circ \), and \( AC=2 \). Let \( M \) be the midpoint of \( AB \). The triangle \( \triangle ACM \) is folded along \( CM \) such that the distance between points \( A \) and \( B \) becomes \( 2\sqrt{2} \). What is the volume of the triangular prism \( A-BCM \)?

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