
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 $a$ and $b$ be two distinct lines, and $\alpha$ and $\beta$ be two distinct planes. Consider the following propositions:  
(1) If $a \parallel \alpha$ and $b \parallel \alpha$, then $a \parallel b$;  
(2) If $a \perp \alpha$ and $b \perp \alpha$, then $a \parallel b$;  
(3) If $a \parallel \alpha$ and $a \parallel \beta$, then $\alpha \parallel \beta$;  
(4) If $a \perp \alpha$ and $a \perp \beta$, then $\alpha \parallel \beta$.  
Among the above propositions, the numbers of all true propositions are     .

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