
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 $ABCD-EFGH$ be a cube with side length 10 units. Let points $I$, $J$, and $K$ be located on edges $\overline{EF}$, $\overline{EH}$, and $\overline{EC}$ respectively, such that $EI = EJ = EK = 3$ units. A tunnel is drilled through the cube such that its sides are planes parallel to $\overline{AE}$, containing the line segments $\overline{IJ}$, $\overline{JK}$, and $\overline{KI}$. Calculate the total surface area of the cube including the internal surface of the tunnel.

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