
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
From a regular tetrahedron with edges of unit length, we cut out four smaller tetrahedrons with planes that bisect the edges starting from the vertices of the base. What is the surface area and volume of the remaining solid?

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