
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
If $a$ and $b$ are two distinct lines, and $\alpha$ and $\beta$ are two distinct planes, then a sufficient but not necessary condition for $\alpha \parallel \beta$ is (fill in all the correct numbers):
1. $a \subset \alpha$, $b \subset \alpha$, $a \parallel \beta$, and $b \parallel \beta$;
2. $a \subset \alpha$, $b \subset \beta$, and $a \parallel b$;
3. $a \perp \alpha$, $b \perp \beta$, and $a \parallel b$;
4. $a \parallel \alpha$, $b \parallel \beta$, and $a \parallel b$.

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