
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
Suppose that  $0^\circ < A < 90^\circ$  and  $0^\circ < B < 90^\circ$  and \[\left(4+\tan^2 A\right)\left(5+\tan^2 B\right) = \sqrt{320}\tan A\tan B\] Determine all possible values of  $\cos A\sin B$ .

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