
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 \( a_1, a_2, \ldots \) and \( b_1, b_2, \ldots \) be arithmetic progressions such that \( a_1 = 20, b_1 = 55 \), and the sum of the 50th terms of both sequences (\( a_{50} + b_{50} \)) is 150.
Find the sum of the first fifty terms of the series \( a_1 + b_1, a_2 + b_2, ... \).
**A)** \( 3750 \)
**B)** \( 7500 \)
**C)** \( 3675 \)
**D)** \( \frac{183750}{49} \)

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