
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 \(a, b, c, d\) be nonzero integers such that
\[
\begin{pmatrix} a & b \\ c & d \end{pmatrix}^2 = \begin{pmatrix} 12 & 0 \\ 0 & 12 \end{pmatrix}.
\]
Find the smallest possible value of \(|a| + |b| + |c| + |d|\).

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