
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 \(c_1 = 50, c_{50} = c_1 + 49d, d_1 = 150, d_{50} = d_1 + 49e\). Given that \(c_{50} + d_{50} = 300\), find the sum of the first fifty terms of the progression \(c_1 + d_1, c_2 + d_2, \ldots, c_{50} + d_{50}\).

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