
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 $\{a_n\}$ is an arithmetic sequence where $$a_1 + a_2 + \cdots + a_{50} = 150 \quad \text{and} \quad a_{51} + a_{52} + \cdots + a_{100} = 250.$$ What is the value of $a_{52} - a_{51}$?

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