
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 \(p=1, 2, \cdots, 10\), let \(S_p\) be the sum of the first \(30\) terms of the arithmetic progression whose first term is \(p\) and whose common difference is \(3p + 1\); compute \(S_1+S_2+\cdots+S_{10}\).
A) 75350
B) 77675
C) 80200
D) 83400
E) 85000

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