
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
A corner of a unit cube is chopped off such that the cut runs through the midpoints of the three edges adjacent to the chosen vertex. What is the height of the remaining solid when the freshly-cut face is placed on a table?

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