
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 $\{\operatorname{det} A: A \in \mathcal{M}\}$, where $\operatorname{det} A$ denotes the determinant of the matrix $A$.

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