
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 $\alpha$ and $\beta$ are two non-intersecting planes, and $m$ and $n$ are two different lines, the correct proposition among the following is ___________.

$①$ If $m$ is parallel to $\alpha$ and $m$ is parallel to $\beta$, then $\alpha$ is parallel to $\beta$

$②$ If $m$ is parallel to $n$ and $m$ is parallel to $\alpha$, then $n$ is parallel to $\alpha$

$③$ If $n$ is a subset of $\alpha$ and $m$ is parallel to $n$, then $m$ is parallel to $\alpha$

$④$ If $m$ is a subset of $\alpha$ and $\alpha$ is parallel to $\beta$, then $m$ is parallel to $\beta$

$⑤$ If $m$ is parallel to $\alpha$ and $n$ is parallel to $\alpha$, then $m$ is parallel to $n$

$⑥$ If $m$ is parallel to $\alpha$ and $n$ is a subset of $\alpha$, then $m$ is parallel to $n$

$⑦$ If $m$ is parallel to $\alpha$, $m$ is a subset of $\beta$, and $\alpha \cap \beta = n$, then $m$ is parallel to $n$

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