
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 an arithmetic sequence $\{a\_n\}$ with a common difference $d \neq 0$, if $a\_5$, $a\_9$, and $a\_15$ form a geometric sequence, what is the value of $\frac{a\_9}{a\_5}$?

A) $\frac{3}{2}$
B) $\frac{2}{3}$
C) $\frac{3}{4}$
D) $\frac{4}{3}$

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