
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
In an $n \times n$ square grid, there are a total of $(n+1)^{2}$ intersection points. The number of squares (which can be tilted) that can be formed using these intersection points as vertices is denoted as $a_{n}$. For example, for $n=2$, $a_{2}=6$; similarly, it can be found that $a_{3}=20$.
1. Find the value of $a_{4}$.
2. Find the value of $a_{n}$.

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