
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
A lattice point  $(x, y, z) \in Z^3$  can be seen from the origin if the line from the origin does not contain any other lattice point  $(x', y', z')$  with   $$ (x')^2 + (y')^2 + (z')^2 < x^2 + y^2 + z^2. $$   Let  $p$  be the probability that a randomly selected point on the cubic lattice  $Z^3$  can be seen from the origin. Given that  $$ \frac{1}{p}= \sum^{\infty}_{n=i} \frac{k}{n^s} $$  for some integers  $ i, k$ , and  $s$ , find  $i, k$  and  $s$ .

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