
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
(1) Simplify $f(x)= \dfrac {\tan (\pi+\alpha)\cos (2\pi+\alpha)\sin (\alpha- \dfrac {\pi}{2})}{\cos (-\alpha -3\pi )\sin (-3\pi -\alpha )}$;  
(2) Given $\tan \alpha= \dfrac {1}{2}$, find the value of $2\sin ^{2}\alpha-\sin \alpha\cos \alpha+\cos ^{2}\alpha$.

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