
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 $0＜α＜\frac{π}{2}$, and $sinα=\frac{4}{5}$．
(1) Find the value of $tanα$;
(2) Find the value of $\frac{{sinαcosα-sin（{π-α}）cos（{α-\frac{{3π}}{2}}）}}{{{{cos}^2}（{α+\frac{π}{2}}）-sin（{α+3π}）cos（{α+π}）}}$.

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