
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 the center of the ellipse $(C)$ is at the origin of the coordinate, its foci are on the $x$-axis, and the maximum and minimum distances from a point on the ellipse $(C)$ to the focus are $3$ and $1$ respectively.

1. Find the standard equation of the ellipse $(C)$;
2. If the line $l: y = x + m$ intersects with the ellipse $(C)$, find the range of values for $m$.

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