
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 two circles C<sub>1</sub> with equation $(x-2\cos\theta)^2+(y-2\sin\theta)^2=1$ and C<sub>2</sub> with equation $x^2+y^2=1$, among the following statements:
① For any value of θ, circle C<sub>1</sub> always touches circle C<sub>2</sub>;
② For any value of θ, there are always four common tangents to circles C<sub>1</sub> and C<sub>2</sub>;
③ When $\theta=\frac{\pi}{6}$, the length of the chord cut off by the line $l: \sqrt{3}x-y-1=0$ on circle C<sub>1</sub> is $\sqrt{3}$;
④ If P and Q are points on circles C<sub>1</sub> and C<sub>2</sub> respectively, then the maximum value of |PQ| is 4.
The correct statement(s) are marked by the sequence number(s) ______.

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