
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
Given three numbers \(a, b, c\). It is known that the arithmetic mean of the numbers \(a\) and \(b\) is 5 greater than the arithmetic mean of all three numbers. The arithmetic mean of the numbers \(a\) and \(c\) is 8 less than the arithmetic mean of all three numbers. How much does the arithmetic mean of the numbers \(b\) and \(c\) differ from the arithmetic mean of all three numbers?

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