
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 the following four propositions: 
1. If $a \parallel \alpha$ and $b \perpendicular \alpha$, then $a \perpendicular b$.
2. If $a \perpendicular b$ and $b \perpendicular \alpha$, then $a \parallel \alpha$.
3. If $a \parallel b$ and $b \perpendicular \alpha$, then $a \perpendicular \alpha$.
4. If $a \perpendicular b$ and $b \parallel \alpha$, then $a \perpendicular \alpha$.

Among these, the correct propositions are.

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