
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 $a$ and $b$ be two non-coincident lines, and $\alpha$ and $\beta$ be two non-coincident planes. Among the following statements, the numbers of all true statements are:

① If $a \parallel \alpha$ and $b \parallel \alpha$, then $a \parallel b$;  
② If $a \perp \alpha$ and $a \perp \beta$, then $\alpha \parallel \beta$;  
③ If $\alpha \perp \beta$, then there must exist a line $l$ such that $l \perp \alpha$ and $l \parallel \beta$;  
④ If $\alpha \perp \beta$, then there must exist a plane $\gamma$ such that $\gamma \perp \alpha$ and $\gamma \perp \beta$.

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