
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
Place real numbers at the vertices of a pentagon such that the sum of the numbers at the ends of one side is 1, at the ends of another side is 2, ..., and at the ends of the last side is 5.

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