
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 pattern are shown, where each line segment represents a toothpick. Initially, each successive stage adds four toothpicks to the previous arrangement. However, starting from the 50th stage and every 50 stages thereafter, the addition rate increases by one toothpick. How many toothpicks are necessary to create the arrangement for the 200th stage?

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