
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 $p,$ $q,$ $r,$ $s$ be nonzero integers such that
\[\begin{pmatrix} p & q \\ r & s \end{pmatrix}^2 = \begin{pmatrix} 9 & 0 \\ 0 & 9 \end{pmatrix}.\]Find the smallest possible value of $|p| + |q| + |r| + |s|$.

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