
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
The following are 5 propositions:  
(1) Let a, b, c be three lines in space. If a⊥c and b⊥c, then a∥b;  
(2) Let a, b be two lines, and α be a plane. If a⊥α and b⊥α, then a∥b;  
(3) Let a be a line, and α, β be two planes. If a⊥β and α⊥β, then a∥α;  
(4) Let α, β be two planes, and c be a line. If c⊥α and c⊥β, then α∥β;  
(5) Let α, β, γ be three planes. If α⊥γ and β⊥γ, then α∥β.  
Among these, the correct propositions are numbered as follows.

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