
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 eccentricity of the ellipse (C) is $\frac{\sqrt{3}}{2}$, the length of the major axis is 4, and the foci are located on the x-axis. The line (l) with a slope of 1 intersects the ellipse (C) at points A and B.
(1) Find the standard equation of the ellipse (C).
(2) Find the maximum value of $|AB|$.

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