
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 vectors $\overrightarrow{a}=(4,5\cos \alpha)$ and $\overrightarrow{b}=(3,-4\tan \alpha)$ with $\alpha\in(0, \dfrac {\pi}{2})$ and $\overrightarrow{a}\perp \overrightarrow{b}$:
1. Find $|\overrightarrow{a}- \overrightarrow{b}|$;
2. Find $\sin (\dfrac {3\pi}{2}+2\alpha)+\cos (2\alpha-\pi)$.

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