
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 $\{b_n\}$ be an arithmetic sequence such that the sum of the first 50 terms is 150, i.e.,
$$
b_1 + b_2 + \cdots + b_{50} = 150,
$$
and the sum of the terms from the 51st to the 100th term is 300, i.e.,
$$
b_{51} + b_{52} + \cdots + b_{100} = 300.
$$
Determine the value of $b_{10} - b_1$.

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