
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 $\frac{x^2}{4} + \frac{y^2}{9} = 1$ and a line $l:\ y = \frac{3}{2}x + m$,
(1) when line $l$ intersects with the ellipse, determine the range of values for the real number $m$;
(2) find the maximum length of the chord that line $l$ cuts from the ellipse.

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