
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
For a circle $\odot O$ with a radius of $R$, the following conclusions are true:<br/>① There are infinitely many $\triangle ABC$ inscribed in $\odot O$, satisfying $\angle ABC=70^{\circ}$, but the length of side $AC$ is uniquely determined;<br/>② There are infinitely many chords $AB$, such that the distance from point $O$ to $AB$ is equal to $d\left(0\leqslant d \lt R\right)$, but the length of $AB$ is uniquely determined;<br/>③ Among all the lines that are externally tangent to $\odot O$, at least one line $l$ exists, where there is a point $P$ on $l$ such that the distance from $P$ to $O$ is equal to $R$.<br/>The correct conclusions among the above are numbered as ______.

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