
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 each integer $p = 2, 3, \cdots, 15$, let $T_p$ be the sum of the first $30$ terms of the arithmetic progression whose first term is $p$ and whose common difference is $3p$. Calculate the total sum $T_2 + T_3 + \cdots + T_{15}$.
A) 155000
B) 156865
C) 157865
D) 158865

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