
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
Suppose $\{b_n\}$ is an arithmetic sequence where 
$$
b_1 + b_2 + \cdots + b_{50} = 150 \quad \text{and} \quad
b_{51} + b_{52} + \cdots + b_{100} = 300.
$$
What is the value of $b_2 - b_1$? Express your answer as a common fraction.

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