
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 that $F\_1$ and $F\_2$ are the left and right foci of the ellipse $\frac{x^2}{4} + \frac{y^2}{3} = 1$, and $M$ is a moving point on the ellipse, there are four conclusions:

1. The maximum value of $|MF\_2|$ is greater than $3$;
2. The maximum value of $|MF\_1| \cdot |MF\_2|$ is $4$;
3. The maximum value of $\angle F\_1MF\_2$ is $60^\circ$;
4. If the moving line $l$ is perpendicular to the $y$-axis and intersects this ellipse at points $A$ and $B$, and $P$ is a point on $l$ satisfying $|PA| \cdot |PB| = 2$, then the trajectory equation of point $P$ is $\frac{x^2}{2} + \frac{2y^2}{3} = 1$ or $\frac{x^2}{6} + \frac{2y^2}{9} = 1$.

The correct sequence numbers for these conclusions are $\_\_\_\_\_\_$.

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