
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 $\frac{x^{2}}{2} + \frac{y^{2}}{6} = 1$ with foci $F\_1$ and $F\_2$, if $\overrightarrow{F\_1M} \cdot \overrightarrow{F\_2M} = 0$, calculate the distance from point $M$ to the $x$-axis.

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