
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 circle $C$: $((x-3)^{2}+(y-4)^{2}=1)$, point $A(0,-1)$, $B(0,1)$, let $P$ be a moving point on circle $C$, and $d=|PA|^{2}+|PB|^{2}$, then the range of $d$ is _____ .

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