
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 $(C)$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$, a square is formed by its two foci and the two vertices on the minor axis. The perimeter of the square is $4\sqrt{2}$.
(1) Find the equation of the ellipse $(C)$;
(2) Let line $(l)$ pass through point $B(0,m)(m > 0)$ and intersect ellipse $(C)$ at points $E$ and $F$. Point $D$ is the symmetric point of point $B$ with respect to the origin. If point $D$ is always inside the circle with line segment $EF$ as its diameter, find the range of $m$.

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