
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
Alexis has  $2020$  paintings, the  $i$ th one of which is a  $1\times i$  rectangle for  $i = 1, 2, \ldots, 2020$ . Compute the smallest integer  $n$  for which they can place all of the paintings onto an  $n\times n$  mahogany table without overlapping or hanging off the table.

*Proposed by Brandon Wang*

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