
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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