
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 $cos(\frac{π}{4}-α)=\frac{3}{5}$ and $sin(\frac{5π}{4}+β)=-\frac{12}{13}$, where $α∈(\frac{π}{4},\frac{3π}{4})$ and $β∈(0,\frac{π}{4})$, find $\frac{tanα}{tanβ}$.

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