
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
Two arithmetic sequences, \(A\) and \(B\), both begin with 30. Sequence \(A\) has a common difference of 8 and is increasing, while sequence \(B\) has a common difference of 12 and is decreasing. What is the absolute value of the difference between the 51st term of sequence \(A\) and the 51st term of sequence \(B\)?

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