
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 an ellipse $(C)$ with its center at the origin $(O)$, its foci on the $x$-axis, and its focal distance equal to the length of its minor axis. A line $(l)$ that does not pass through the origin intersects the ellipse $(C)$ at points $M$ and $N$. The slopes of the lines $OM$, $MN$, and $ON$ form a geometric sequence.

1. Find the eccentricity of the ellipse $(C)$.
2. If the ellipse $(C)$ passes through the point $(2,0)$, find the maximum area of $\triangle OMN$.

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