
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 $m$ and $n$ are two non-intersecting lines, and $\alpha$, $\beta$, and $\gamma$ are three distinct planes. The following propositions are given:
1. If $m \perp \alpha$ and $n \parallel \alpha$, then $m \perp n$.
2. If $\alpha \parallel \beta$, $\beta \parallel \gamma$, and $m \perp \alpha$, then $m \perp \gamma$.
3. If $m \parallel \alpha$ and $n \parallel \alpha$, then $m \parallel n$.
4. If $\alpha \perp \gamma$ and $\beta \perp \gamma$, then $\alpha \parallel \beta$.

Find the sequence number(s) of the correct proposition(s). (Fill in the sequence number(s) of the proposition(s) you believe to be correct)

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