
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 $\alpha$, $\beta$, and $\gamma$ be planes, given the following conditions: ① $a$ and $b$ are skew lines, $a \subset \alpha$, $b \subset \beta$; $a \parallel \beta$, $b \parallel \alpha$; ② Three non-collinear points in $\alpha$ are equidistant from $\beta$; ③ $\alpha \perp \gamma$, $\beta \perp \gamma$. Among these conditions, the number of conditions that can make $\alpha \parallel \beta$ true is.

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