
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
The center of a cube is reflected off all its faces, and the 6 points obtained, together with the vertices of the cube, determine 14 vertices of a polyhedron, all 12 faces of which are congruent rhombuses. (This polyhedron is called a rhombic dodecahedron—a shape naturally occurring in garnet single crystals.) Calculate the surface area and volume of the constructed polyhedron if the edge of the original cube has a length of \( a \).

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