
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 triangle $△ABC$, such that $BC⋅AC=2\sqrt{2}$, if $C=\frac{3π}{4}$ and $\frac{\sin A}{\sin B}=\frac{1}{2\cos (A+B)}$, then $AB=$ \_\_\_\_\_\_.

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