
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 that $\{b_n\}$ is an arithmetic sequence where the sum of the first 50 terms is 150, i.e., 
$$
b_1+b_2+ \cdots +b_{50}=150,
$$ 
and the sum of terms from 51 to 100 is 300, i.e.,
$$
b_{51}+b_{52}+ \cdots + b_{100}=300.
$$
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}
user