
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
Find all triples  $(a,b,c)$  of real numbers such that the following system holds:  $$ \begin{cases} a+b+c=\frac{1}{a}+\frac{1}{b}+\frac{1}{c} a^2+b^2+c^2=\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\end{cases} $$  *Proposed by Dorlir Ahmeti, Albania*

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