
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 parabola $y=x^{2}$ and its tangent line $m$ at point $A(2,4)$.
(1) Find the equation of the tangent line $m$;
(2) If the tangent line $m$ passes through one focus and the lower vertex of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$, find the equation of this ellipse.

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