
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
Given that \( a_1 = 25 \), \( b_1 = 75 \), and \( a_{100} + b_{100} = 100 \), find the sum of the first 100 terms of the sequence \(\{a_n + b_n\}\), denoted \(S_{100}\).

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