
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 lines a, b, c, and planes α, β, γ, consider the following propositions:  
① If α is parallel to β and β is parallel to γ, then α is parallel to γ.  
② If a is parallel to b is parallel to c, and α is perpendicular to a, β is perpendicular to b, γ is perpendicular to c, then α is parallel to β is parallel to γ.  
③ If a is parallel to b is parallel to c, and a is parallel to α, b is parallel to β, c is parallel to γ, then α is parallel to β is parallel to γ.  
④ If a is perpendicular to α, b is perpendicular to β, c is perpendicular to γ, and α is parallel to β is parallel to γ, then a is parallel to b is parallel to c.  
Among these propositions, the correct ones are ______________.

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