
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
Three arithmetic sequences $A$, $B$, and $C$ all begin with 40. Sequence $A$ has a common difference of 8 and is increasing, sequence $B$ has a common difference of -12 and is decreasing, and sequence $C$ has a common difference of -5 and is decreasing. What is the absolute value of the difference between the 51st term of sequence $A$ and the 51st term of sequence $C$?

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