
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 circle $C: (x-3)^2 + (y-4)^2 = 1$, and points $A(-1,0)$, $B(1,0)$, let point $P$ be a moving point on the circle. Then, the maximum and minimum values of $d = |PA|^2 + |PB|^2$ are \_\_\_\_\_\_\_\_ and \_\_\_\_\_\_\_\_, respectively.

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