
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 ellipse $C: \frac{x^{2}}{16}+ \frac{y^{2}}{7}=1$, $F$ is the right focus of the ellipse, $B$ is the upper vertex of the ellipse, and $P$ is a moving point on the ellipse.
(1) Find the range of $|OP|^{2}+|PF|^{2}$
(2) Given the line $l$: $x+y=1$, $P$ is a point on the ellipse and $d$ is the distance from point $P$ to line $l$, find the range of $d$.

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