
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
Let the base of the rectangular prism $A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ be a rhombus with an area of $2 \sqrt{3}$ and $\angle ABC = 60^\circ$. Points $E$ and $F$ lie on edges $CC'$ and $BB'$, respectively, such that $EC = BC = 2FB$. Find the volume of the pyramid $A-BCFE$.

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