
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 a cube, the centers of the bases are connected to the centers of the lateral faces. Calculate the surface area of the resulting octahedron if the edge of the cube is equal to \( a \).

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