
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 that 6 rational numbers are placed sequentially on a given circle, now select any 3 adjacent numbers $a$, $b$, $c$ in a clockwise direction, satisfying $a = |b - c|$. It is also known that the total sum of all the placed numbers is 1. What are the values of these 6 numbers?

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