
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 the ellipse $\frac{x^2}{4} + \frac{y^2}{2} = 1$ with left and right foci $F\_1$ and $F\_2$, a line $l$ passing through $F\_2$ at a 45° angle intersects the ellipse at points $A$ and $B$. Among the following statements, the sequence number(s) of all correct ones are:
1. The perimeter of $\triangle ABF_1$ is 8;
2. The distance from the origin to $l$ is 1;
3. $|AB|=\frac{8}{3}$;

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