
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
Definition: If for any positive number $T$, there exists a non-zero constant $m$ such that the function $y=f(x)$ defined on $R$ satisfies $\frac{{f(x+T)}}{{f(x)}}=m$ for any real number $x$, then the function $y=f(x)$ is called a "$\xi$ function." Among the four functions $y=2x+1$, $y=(\frac{1}{2})^{3x-2}$, $y=x^{3}$, $y=\ln(x-1)$, which of them is a "$\xi$ function"? (Only fill in the serial number).

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