
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
Determine all triplets  $(a,b,c)$  of real numbers such that sets  $\{a^2-4c, b^2-2a, c^2-2b \}$  and  $\{a-c,b-4c,a+b\}$  are equal and  $2a+2b+6=5c$ . In every set all elements are pairwise distinct

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