
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 (E) with the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ that passes through the focus of the parabola $y^2 = 16x$ and shares the same foci with the hyperbola $x^2 - y^2 = 2$.
1. Find the standard equation of the ellipse (E).
2. Let point $M(m, 0)$ be on the major axis of the ellipse (E), and point $P$ be any point on the ellipse. When the distance $| \overrightarrow{MP} |$ is at its minimum, point $P$ coincides with the right vertex of the ellipse. Find the range of possible values for the real number $m$.

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