
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 $ABCDEF$ be a cube with edge length $10$. Points $M$, $N$, and $O$ are on edges $AB$, $AD$, and $AE$ respectively such that $AM = AN = AO = 3$. A solid $T$ is obtained by removing a triangular pyramid from vertex $A$, with the pyramid having its other vertices at $M$, $N$, and $O$. Find the total surface area of $T$, expressed in terms of integers and simple radicals.

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