
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  $\mathcal{M}$  be the set of all  $2021 \times 2021$  matrices with at most two entries in each row equal to  $1$  and all other entries equal to  $0$ .
Determine the size of the set  $\{ \det A : A \in M \}$ .
*Here  $\det A$  denotes the determinant of the matrix  $A$ .*

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