
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
$\alpha$ and $\beta$ are two distinct planes. The following conditions can determine that $\alpha \parallel \beta$:  
(1) Both $\alpha$ and $\beta$ are parallel to lines $l$ and $m$;  
(2) There are three non-collinear points in $\alpha$ that are equidistant from $\beta$;  
(3) $l$ and $m$ are two lines within $\alpha$, and both are parallel to $\beta$;  
(4) $l$ and $m$ are two skew lines, and both are parallel to $\alpha$ and $\beta$.

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