
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 $\{a_n\}$ is an arithmetic sequence with $$
a_1 + a_2 + \cdots + a_{50} = 50 \quad \text{and} \quad
a_{51} + a_{52} + \cdots + a_{100}=150.
$$
What is the value of $a_2 - a_1$?

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