
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
Let $a_{1}$, $a_{2}$, $\ldots$, $a_{n}$ be a sequence of $n$ terms with common difference $d \neq 0$, where $n \geqslant 4$. If after removing one term from this sequence, the remaining terms (in the original order) form a geometric sequence, then the set of all pairs of numbers $({n, \frac{a_1}{d}})$ is ____.

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