
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
Given a matrix $\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22}\end{pmatrix}$ satisfies: $a_{11}$, $a_{12}$, $a_{21}$, $a_{22} \in \{0,1\}$, and $\begin{vmatrix} a_{11} & a_{12} \\ a_{21} & a_{22}\end{vmatrix} =0$, determine the total number of distinct matrices.

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