
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 $a$, $b$, and $c$ represent three different lines, and let $y$ represent a plane. Consider the following propositions:  
① If $a \parallel b$ and $b \parallel c$, then $a \parallel c$.  
② If $a \perp b$ and $b \perp c$, then $a \perp c$.  
③ If $a \parallel y$ and $b \parallel y$, then $a \parallel b$.  
④ If $a \perp y$ and $b \perp y$, then $a \parallel b$.  
Identify the true propositions among these.

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