
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 corner of a cube with side length 2 is chopped off such that the cut runs through the three vertices adjacent to the vertex of the chosen corner. Once the cube has its freshly-cut face placed on a table, it is then rotated to rest on one of the original faces of the cube. What is the height of the remaining cube from the table to the highest point?

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