
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 two circles $C_{1}: (x-1)^{2}+y^{2}=25$ and $C_{2}: (x+1)^{2}+y^{2}=1$, a moving circle $C_{3}$ is tangent to the inside of circle $C_{1}$ and to the outside of circle $C_{2}$.
(1) Let the trajectory of the center of moving circle $C_{3}$ be curve $C$. Find the equation of $C$.
(2) If a line $l$ passing through point $A(0,-3)$ intersects with curve $C$ at two points $D$ and $E$, find the maximum area of $\triangle ODE$.

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