
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
The first three stages of a geometric pattern are shown, where each line segment of toothpick forms a growing square grid. Each stage adds layers to the grid in a pattern such that each successive stage squares the number of lines required for a complete layer. If the pattern continues such that at the first stage, one needs 8 toothpicks, that form a shape of a square, then each new stage requires that each side of the square increases by 4 toothpicks more than the extra toothpicks needed for each side in the previous stage, how many toothpicks are necessary to create the arrangement for the 20th stage?

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