
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 two distinct lines $a$ and $b$, and two distinct planes $\alpha$ and $\beta$, examine the validity of the following propositions:
1. If $a \parallel b$ and $b \parallel \alpha$, then $a \parallel \alpha$.
2. If $a, b \subset \alpha$ and $a \parallel \beta$, $b \parallel \beta$, then $\alpha \parallel \beta$.
3. If $a \perp \alpha$ and $b \parallel \alpha$, then $a \perp b$.
Identify the correct propositions.

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