
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
If the inverse proportion function $y=\frac{5}{x}$ intersects with the direct proportion function $y=kx$ at points $A$ and $B$, and $A(x_{1}$,$y_{1})$,$B(x_{2}$,$y_{2})$, then $(x_{1}-2x_{2})(3y_{1}+4y_{2})=\_\_\_\_\_\_.$

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