
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
Let
\[
\mathbf{N} = \begin{pmatrix} a & b & c & d \\ b & c & d & a \\ c & d & a & b \\ d & a & b & c \end{pmatrix}
\]
be a 4x4 matrix with complex entries where \( \mathbf{N}^2 = \mathbf{I} \). If \( abcd = 1 \), find the possible values of \( a^4 + b^4 + c^4 + d^4 \).

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