
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 $\alpha$ and $\beta$ are two different planes, and $a$ and $b$ are two different lines, with the conditions: ① $\alpha \cap \beta = \emptyset$; ② $a \perp \alpha$, $a \perp \beta$; ③ $a \parallel \alpha$, $b \parallel \alpha$, $b \subset \beta$. Among these conditions, which ones can deduce that plane $\alpha$ is parallel to plane $\beta$? (Fill in the serial number).

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