
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
Let \( c_1, c_2, \ldots \) and \( d_1, d_2, \ldots \) be arithmetic progressions with \( c_1 = 15, d_1 = 105 \), and \( c_{100} + d_{100} = 300 \). Find the sum of the first hundred terms of the progression \( c_1 + d_1, c_2 + d_2, \ldots \).
**A)** 9000
**B)** 15000
**C)** 18000
**D)** 21000

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