
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
Nathan has discovered a new way to construct chocolate bars, but it’s expensive! He starts with a single  $1\times1$  square of chocolate and then adds more rows and columns from there. If his current bar has dimensions  $w\times h$  ( $w$  columns and  $h$  rows), then it costs  $w^2$  dollars to add another row and  $h^2$  dollars to add another column. What is the minimum cost to get his chocolate bar to size  $20\times20$ ?

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