
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 curve $C$: $|x|+|y|=m (m > 0)$.
(1) If $m=1$, find the area of the shape enclosed by curve $C$.
(2) Find the range of values for the real number $m$ such that the curve $C$ intersects with the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ at four distinct points.

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