
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
For \( p = 1, 2, \dots, 10 \), let \( S_p \) be the sum of the first 50 terms of the arithmetic progression whose first term is \( p \) and whose common difference is \( 2p \); then \( S_1 + S_2 + \cdots + S_{10} \) equals?
A) 120000
B) 130000
C) 137500
D) 140000

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