
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 \(\mathbf{A} = \begin{pmatrix} a & 2 \\ -3 & d \end{pmatrix}\) for some real numbers \(a\) and \(d.\) If
\[\mathbf{A} + \mathbf{A}^{-1} = \mathbf{0},\] then find \(\det \mathbf{A}.\)

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