
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 \(a\) and \(b\) represent two different lines, and \(\alpha\), \(\beta\), \(\gamma\) represent three non-coincident planes, the following propositions are given:  
1. If \(\alpha \cap \gamma = a\), \(\beta \cap \gamma = b\), and \(a \parallel b\), then \(\alpha \parallel \beta\);
2. If \(a\) and \(b\) intersect and both are outside \(\alpha\) and \(\beta\), with \(a \parallel \alpha\), \(b \parallel \alpha\), \(a \parallel \beta\), \(b \parallel \beta\), then \(\alpha \parallel \beta\);
3. If \(a \subset \alpha\), \(a \parallel \beta\), and \(\alpha \cap \beta = b\), then \(a \parallel b\).  
The correct proposition(s) is/are \_\_\_\_\_\_.

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