
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 line $a$ and two planes $\alpha$ and $\beta$, consider the following four propositions:  
① If $a \parallel \alpha$, then any line within $\alpha$ is parallel to $a$;  
② If $a \perp \alpha$, then any line within $\alpha$ is perpendicular to $a$;  
③ If $\alpha \parallel \beta$, then any line within $\beta$ is parallel to $\alpha$;  
④ If $\alpha \perp \beta$, then any line within $\beta$ is perpendicular to $\alpha$.  
Among these, the true propositions are     .

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