
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 $\alpha$, $\beta$, $\gamma$, there are the following four propositions:  
① If $a \subset \alpha$, $b \subset \alpha$, $c \perp a$, $c \perp b$ then $c \perp \alpha$;  
② If $b \subset \alpha$, $a \parallel b$, then $a \parallel \alpha$;  
③ If $a \parallel \alpha$, $\alpha \cap \beta = b$, then $a \parallel b$;  
④ If $a \perp \alpha$, $b \perp \alpha$, then $a \parallel b$;  
Among these, the correct proposition(s) is/are.

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