
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 $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$ and the line $l: y = \frac{3}{2}x + m$,
(1) Find the range of real number $m$ when the line $l$ intersects with the ellipse;
(2) Find the maximum length of the chord cut by the line $l$ on the ellipse.

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