
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 new pattern are displayed below, and each line segment represents a toothpick. In this modified pattern, the arrangement begins with 5 toothpicks in the first stage. At each successive stage, five more toothpicks are added to the previous arrangement. Exceptionally, every 50th stage doubles the number of toothpicks from the total accumulated in the stage before it. How many toothpicks are required to create the arrangement for the 250th stage?

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