
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
(1) Given an ellipse passes through point A $(0, \frac{5}{3})$ and B $(1, 1)$, find the standard equation of the ellipse.  
(2) If a point M on the parabola $y^2 = 2px$ ($p > 0$) has distances of 10 and 6 from the focus and the axis of symmetry, respectively, find the equation of the parabola.

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