
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 that $a$ and $b$ are two non-coincident lines, and $\alpha$, $\beta$, $\gamma$ are three pairwise non-coincident planes, the following four propositions are provided:
① If $a \perp \alpha$ and $a \perp \beta$, then $\alpha \parallel \beta$;
② If $\alpha \perp \gamma$ and $\beta \perp \gamma$, then $\alpha \parallel \beta$;
③ If $\alpha \parallel \beta$, $a \subset \alpha$, and $b \subset \beta$, then $a \parallel b$;
④ If $\alpha \parallel \beta$, $\alpha \cap \gamma = a$, and $\beta \cap \gamma = b$, then $a \parallel b$.
Identify the correct propositions.

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