
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
Let $l$ and $m$ be two different lines, and $a$ be a plane. There are the following four propositions:  
(1) If $l \perp a$ and $m \subset a$, then $l \perp m$;  
(2) If $l \perp a$ and $l \parallel m$, then $m \perp a$;  
(3) If $l \parallel a$ and $m \subset a$, then $l \parallel m$;  
(4) If $l \parallel a$ and $m \parallel a$, then $l \parallel m$.  
Among these propositions, the correct ones are ____.

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