
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
Consider a cube of edge length 2 units. A corner of this cube is chopped off such that the cut runs through the three vertices adjacent to the vertex of the chosen corner. What is the height of the remaining cube when the freshly-cut face, which is an equilateral triangle, is placed on a table?

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