
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 $f(x) = \sin x + mx$ where $m \in \mathbb{R}$. Four conclusions are given as follows:<br/>① Regardless of the value of $m$, the curve $y = f(x)$ always has two parallel tangent lines;<br/>② Regardless of the value of $m$, the curve $y = f(x)$ always has two perpendicular tangent lines;<br/>③ Regardless of the value of $m$, there always exists an infinite sequence $\{a_{n}\}$ such that the tangent lines of the curve $y = f(x)$ at $x = a_{n}$ $(n = 1, 2, 3, \cdots)$ are parallel to each other;<br/>④ Regardless of the value of $m$, there always exists an infinite sequence $\{a_{n}\}$ such that the tangent lines of the curve $y = f(x)$ at $x = a_{n}$ $(n = 1, 2, 3, \cdots)$ are the same straight line.<br/>The correct numbers of the conclusions are ____.

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