
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 the function $f(x)=\log_{2}\frac{x}{2}\cdot\log_{2}\frac{x}{8}$, if $f(x_{1})=f(x_{2})$ (where $x_{1}\neq x_{2}$), determine the minimum value of $\frac{13}{x_{1}}+\frac{16}{x_{2}}$.

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