
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
(1) Find the range of $k$ such that the curve $C$: $\frac{x^2}{4-k} - \frac{y^2}{1-k} = 1$ represents an ellipse with foci on the $x$-axis.
(2) Find the standard equation of the ellipse with foci at $F\_1(-2,0)$ and $F\_2(2,0)$, and passing through the point $M(\sqrt{6}, 2)$.

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