
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 a rectangular prism \( ABCD-A'B'C'D' \) with a rhombus base, where the base area is \( 2 \sqrt{3} \), and \( \angle ABC = 60^\circ \). Let \( E \) and \( F \) be points on edges \( CC' \) and \( BB' \) respectively, such that \( EC = BC = 2FB \). Determine the volume of the pyramid \( A-BCEF \).

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