
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 non-zero $n$-term arithmetic sequence with $n \geq 4$ and a non-zero common difference $d$. If removing one term from this sequence results in a geometric sequence (in the original order), then the set of all pairs $$(n, \frac {a_{1}}{d})$$ is \_\_\_\_\_\_\_\_\_\_\_.

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