
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 $m$ and $n$ be two lines in space, and let $\alpha$ and $\beta$ be two planes in space. Consider the following propositions:
(1) If $m \parallel \alpha$ and $m \parallel \beta$, then $\alpha \parallel \beta$;
(2) If $m \perp \alpha$ and $m \perp \beta$, then $\alpha \parallel \beta$;
(3) If $m \parallel \alpha$ and $n \parallel \alpha$, then $m \parallel n$;
(4) If $m \perp \alpha$ and $n \perp \alpha$, then $m \parallel n$.
Among the above propositions, the sequence numbers of all true propositions are ____.

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