
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 \( T_p \) be the sum of the first \( 50 \) terms of the arithmetic progression whose first term is \( 2p \) and the common difference is \( 2p + 1 \). Calculate \( T_1 + T_2 + \cdots + T_{10} \).
A) 140250
B) 150000
C) 152500
D) 155000

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