
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 $m$ and $n$ be two different lines, and $\alpha$, $\beta$, $\gamma$ be three different planes. The following four propositions are given:<br/>① If $m$ is parallel to $\alpha$ and $n$ is parallel to $\alpha$, then $m$ is parallel to $n$;<br/>② If $\alpha$ is perpendicular to $\gamma$ and $\beta$ is perpendicular to $\gamma$, then $\alpha$ is parallel to $\beta$;<br/>③ If $m$ is perpendicular to $\alpha$ and $n$ is parallel to $\alpha$, then $m$ is perpendicular to $n$;<br/>④ If $\alpha$ is parallel to $\beta$, $\beta$ is parallel to $\gamma$, and $m$ is perpendicular to $\alpha$, then $m$ is perpendicular to $\gamma$;<br/>The correct propositions are ____.

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