
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
In space, consider the following propositions: \\
(1) If line $m$ is parallel to a line in plane $\alpha$, then $m \parallel \alpha$; \\
(2) If plane $\alpha \perp \beta$ and $\alpha \cap \beta = l$, then a line passing through a point $P$ in $\alpha$ and perpendicular to $l$ is perpendicular to plane $\beta$; \\
(3) If line $a \parallel b$, and line $l \perp \alpha$, then $l \perp b$. \\
Among these propositions, the correct one(s) is(are) __________. (Write down the number(s) of the proposition(s))

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