
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 that $m$ and $n$ represent different lines, and $\alpha$ and $\beta$ represent different planes, then among the following statements, the true ones are numbered __________  
$(1)$ If $m \perp \alpha$ and $n \perp \alpha$, then $m \parallel n$  
$(2)$ If $m \perp n$ and $n \perp \alpha$, then $m \parallel \alpha$  
$(3)$ If $m \perp \alpha$ and $m \perp \beta$, then $\alpha \parallel \beta$

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