
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 cube $ABCD.EFGH$ where each edge of the cube is 10 units long. Let $P$, $Q$, and $R$, be points on edges $\overline{AB}$, $\overline{AD}$, and $\overline{AE}$, respectively, such that $PA = QA = RA = 3$ units. A tunnel is cut through the cube, the sides of which are in planes parallel to the diagonal $\overline{AG}$, and contain edges $\overline{PQ}$, $\overline{QR}$, and $\overline{RP}$. Calculate the surface area of the remaining solid $T$.

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