
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
We construct 5 regular tetrahedrons on a square \( N \), where each of the faces of the tetrahedrons is inclined at the same angle to the base plane. The bases of four of the tetrahedrons are the four smaller squares obtained by dividing \( N \) along its two medians, and the base square of the fifth tetrahedron has its vertices at the midpoints of \( N \)'s sides. Calculate the volume of the space filled by the 5 tetrahedrons.

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