
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 $\mathbf{B}$ be a $2 \times 2$ matrix, with real entries, such that $\mathbf{B}^4 = \mathbf{0}.$  Determine the number of different possible matrices that $\mathbf{B}^2$ can be.  If you think the answer is infinite, then enter "infinite".

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