
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
If a straight line $l$ and a curve $C$ satisfy the following two conditions: (i) The line $l$ is tangent to the curve $C$ at the point $P(x_0, y_0)$; (ii) The curve $C$ lies on both sides of the line $l$ near point $P$, then the line $l$ is said to "cross-tangentially" the curve $C$ at point $P$. The correct statements among the following are _____ (Write down the number of all correct statements):

① The line $l: y=0$ "cross-tangentially" intersects the curve $C: y=x^3$ at the point $P(0, 0)$;

② The line $l: x=-1$ "cross-tangentially" intersects the curve $C: y=(x+1)^2$ at the point $P(-1, 0)$;

③ The line $l: y=x$ "cross-tangentially" intersects the curve $C: y=\sin x$ at the point $P(0, 0)$;

④ The line $l: y=x$ "cross-tangentially" intersects the curve $C: y=\tan x$ at the point $P(0, 0)$.

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