
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 that $\tan (\pi+\alpha)=- \frac {1}{2}$, find the value of the following expressions:

$(1) \frac {2\cos (\pi-\alpha)-3\sin (\pi+\alpha)}{4\cos (\alpha-2\pi)+\cos ( \frac {3\pi}{2}-\alpha)}$;

$(2)\sin ^{2}\alpha-2\sin \alpha\cos \alpha+4\cos ^{2}\alpha$

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