
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
Given $a_1$, $a_2$, $a_3$, $a_4$ form an arithmetic sequence with each term being non-zero and the common difference $d \neq 0$, and removing one term results in a geometric sequence, find the value of $\frac{a_1}{d}$.

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