
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
\[\mathbf{M} = \begin{pmatrix} a & b & c & d \\ b & c & d & a \\ c & d & a & b \\ d & a & b & c \end{pmatrix}\]
be a matrix with complex entries such that $\mathbf{M}^2 = \mathbf{I}$. 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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