
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
(1) In the first quadrant of the Cartesian coordinate system, there are \((n+1)^{2}\) grid points with coordinates \((i, j)\) where \(i, j \in \mathbb{Z}\) and \(1 \leqslant i, j \leqslant n\). Find the number of squares that can be formed with these grid points as vertices (the squares can be tilted).

(2) In space, is it possible to have a cube whose vertices are grid points and whose edges are not parallel to the coordinate axes?

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